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Specifically for teenagers it may be important to work out in both aerobic and anaerobic workouts. So, this would be another reason to favor the combined over the other regimen.

You will probably have overheard the "knowledgeable" trainers at the gym tell their credulous clients, who just told them they "want to lose that belly fat", that the best thing they could do was to "stop spending that much time with weight training" and to do some more (steady state) cardio. Well, in general, there's nothing wrong about steady state cardio - in fact, many studies show that it is superior to resistance training when it comes to "merely" shedding body weight (in the obese). If "weight loss" is still everything you're aspiring, though, you are either new to the waredownloadsoft or another of the "headline skimmers" who happen to ask questions that are answered not just in the article, but actually in one of the red boxes... ah, I am digressing.

So, what I actually wanted to tell you is that a recent study from the Universities of Ottawa and Calgary (Alberta. 2015), clearly contradicts the average commercial gym chain trainer's recommendation and shows that belly fat loss is better achieved with diet + resistance training.
The subjects of the study were youngsters, 304 (! the high number of participants is a huge plus of the study) 14-18 year-old overweight and obese teenagers (mean body fat almost 50%!), to be specific, who were randomized to four different treatments for 22 weeks:

Table 1: Training progression in the Aerobic and Resistance group (Alberga. 2015)

• aerobic training (Aerobic), 
• resistance training (Resistance),
• combined aerobic + resistance training (Combined) or 
• non-exercising control group (Control)

Adolescents,... ok, but unless they're too sarcopenic (=suffer from pronounced age-induced muscle loss) to hit the weights, your overweight clients or you, yourself, should be able to follow the same training programs the adolescents did and see similar results if you fully adhere to the following training prescriptions:

• Resistance: The duration of each session progressed to a maximum of about 45 min. Exercises were primarily performed on weight machines, and when required with dumbbells (lateral raise, shrugs, bicep curls, front raise, preacher curl, dumbbell pullover) or by using one's own body weight as resistance (lunges, sit-ups and abdominal crunches).
  

  Table 2: Overview of the individual workouts in the Resistance group (Alberga. 2015).

  Participants alternated among exercises from groups A1, A2, B1 and B2 shown in Table 2. Participants were asked to rest for ~ 2 min between sets and were instructed on proper breathing techniques.
• Aerobic: Participants randomized to the aerobic training group underwent a 22-week program (Table 1, left) wherein the exercise intensity and duration increased progressively to a maximum of 45 min per session. Exercise was performed on a cycle ergometer, elliptical or treadmill and participants were free to vary the machine(s) used. Exercise intensity was standardized using heart rate monitors (Polar Electro Oy, Kempele, Finland).
• Combined: This group performed the full exercise programs done by both the aerobic and resistance training groups (Table 1, left + right) during each session for a total of 4 times per week for a maximum of 90 min per session.

Figure 1: Changes in subcutaneous (SAT) and visceral (VAT) body fat at different regions; L4L5 represents area between 4th and 5th Lumbar vertebrae; * indicates sign. difference to control; # sign. difference to aerobic (Alberga. 2015).

References:

• Alberga, A. S., et al. "Effects of aerobic and resistance training on abdominal fat, apolipoproteins and high-sensitivity C-reactive protein in adolescents with obesity: the HEARTY randomized clinical trial." International journal of obesity (2005) (2015).
• Dansinger, Michael L., et al. "Comparison of the Atkins, Ornish, Weight Watchers, and Zone diets for weight loss and heart disease risk reduction: a randomized trial." Jama 293.1 (2005): 43-53.
• Thompson, A., and J. Danesh. "Associations between apolipoprotein B, apolipoprotein AI, the apolipoprotein B/AI ratio and coronary heart disease: a literature‐based meta‐analysis of prospective studies." Journal of internal medicine 259.5 (2006): 481-492.
• Walldius, G., and I. Jungner. "The apoB/apoA‐I ratio: a strong, new risk factor for cardiovascular disease and a target for lipid‐lowering therapy–a review of the evidence." Journal of internal medicine 259.5 (2006): 493-519.

I can almost guarantee that the results of this study are not sex-specific. Ladies, pick up the weights fater you hit the treadmill, stairmaster, elliptical or other torture instrument you like to use!

It has been a while since the last study on exercise order (cardio or weights first) has been published. Now, scientists from the University of Kurdistan have conducted another study to investigate the effects of intrasession sequencing of concurrent resistance and endurance training on the serum leptin, testosterone, cortisol responses and body composition in obese men.

And don't worry, we are not talking about useless acute-phase data that shows no correlation with either strength or muscle gains, or fat loss (West. 2012). Sheikholeslami-Vatani and colleagues conducted an eight-week study on thirty obese young male students without continuous exercise history (age: 23.2±1.4 year, BMI: 31.8±1.6 kg/m²).
The subjects were randomly divided into three groups: concurrent resistance-endurance (CRE, n = 10) group, concurrent endurance-resistance (CER, n = 10) group and control (C, n = 10) group (no training program). The concurrent training groups (CER and CRE) trained three times a week on alternate days for 8 weeks. The training itself consisted of which consisted of ...

"running with 70—75% of maximal heart rate (HRmax) for 10 minutes which gradually increased to 80% HRmax for 21.5 minutes [plus] resistance training consisted of 3 sets of 8 repetitions at 80% of 1 repetition maximum (1RM) in 5 resistance exercises (leg extensions, lying leg curl, triceps pushdown, bench press and lateral pull down)" (Sheikholeslami-Vatani. 2015). 

In-between the endurance and resistance (or vice versa) training parts of the workouts, the subjects rested for 5 minutes. Blood sampling and skin-fold measurements to asses the body composition was conducted 48 hours before the start of the course and again 48 hours after the last training session (learn why waiting longer for the body comp test may have been better, but no study does that).

Figure 1: Relative changes in hormone levels (left) and absolute and relative changes in body fat fat free mass and body fat % (right) after 8 weeks of doing nothing (C) or doing cardio (CER) or weights (CRE) first (Sheikholeslami-Vatani. 2015).

I've plotted the most important results in Figure 1a & b. So, let's take a look: The first thing that everyone should see is that both workout regimen had relevant health and physique effects:

• Similar gains w/ weights vs. cardio first in trained men | more.

  normalization of leptin levels (health)
• slight increases in testosterone (health)
• increases in cortisol (which are benign | learn why)
• significant reductions in body fat (health + physique)
• increases in fat free mass (health and physique)

References:

• Sheikholeslami-Vatani, D., et al. "The effect of concurrent training order on hormonal responses and body composition in obese men." Science & Sports (2015).
• West, Daniel WD, and Stuart M. Phillips. "Associations of exercise-induced hormone profiles and gains in strength and hypertrophy in a large cohort after weight training." European journal of applied physiology 112.7 (2012): 2693-2702.

Just look at the guys surrounding you, girls. How on earth will you get bulky if they are training like maniacs and still look like size-zero bans?

"Overfat", that's a term scientists use to refer to obese, but more importantly over- or even normal-weight people who are still carrying exuberant amounts of body fat around. In a recent meta-analysis, James E. Clark from the Manchester Community College tried to figure out, which of the significant numbers of means of methods to alter body composition, and metabolic issues that are available for the adult who is overfat is the "best" one.

In his review, the scientists focused on comparing changes from treatment program for adults who are overfat based on analysis of aggregated effect size (ES) of inducing changes from 66-population based studies, and 162-studywise groups.
Clark's analysis of this large dataset yielded both, obvious and less obvious results. The realization that "a hypocaloric balance [=dietary restriction] is necessary for changing body composition" (Clark. 2015), for example is hardly surprising.

Figure 1: There's little doubt that the overall improvements in body composition (figures are effect sizes for loss of fat, increase in lean mass) are the most pronounced in response to diet + resistance training (but non-existent w/ resistance training, only - not shown). What is surprising is the low efficacy of combined training programs, though (Clark. 2015).

What may be surprising, though is the fact that the available evidence indicates that the size and effectiveness of the caloric deficit "does not equate with the effectiveness for body compositional changes, or any biomarkers associated with metabolic issues" (Clark. 2015). In other words: It's not the guy or gal who diets the hardest who will lose the largest amounts of body fat.

Figure 2: The effect sizes of the interventions' effects on insulin, leptin, cholesterol & co yields similar results: The combination of resistance training and diet has (on average) the most favorable effects (Clark. 2015).

As the data in Figure 1 goes to show you, the combination with exercise is generally beneficial. In view of the fact that being "overfat" is also associated with being undermuscled, there's yet no reason to doubt Clark's conclusion that

"resistance training (RT) was more effective than endurance training (ET) or combination of RT and ET, particularly when progressive training volume of 2-to-3 sets for 6-to-10 reps at an intensity of ≥75% 1RM, utilizing whole body and free-weight exercises, at altering body compositional measures (ES of 0.47, 0.30, and 0.40 for loss of BM, FM, and retention of FFM respectively)" (Clark. 2015)

Now, while this may still be in line with at least some of the mainstream recommendations, Clark's observation that the RT regimen was also more effective at reducing total cholesterol (ES = 0.85), triglycerides (ES = 0.86) and low-density lipoproteins (ES = 0.60), as well as at reducing fasting insulin levels (ES = 3.5) than endurance training or  endurance training and resistance training in combination emphasizes how much of a game changer (intense!) resistance training can actually be.

Figure 3: The good results some studies on combined training show suggest that the lack of benefits in the meta-analysis may be a statistical phenomenon, or a result of certain aspects of the individual study design (e.g. low volume or intensity) in some of the studies (data from Donnely. 1991).

There's thus just one thing we still have to address: Why is doing both, cardio and resistance training not more effective? Well, the answer may be hidden in the study design, where the combination training rarely complied to the previously outlined rules of a high intensity, progressive, high volume resistance training workout with free weights. In addition studies that met these criteria, such as Cuff et al. (2003), for example, didn't measure the body composition of their female subjects and focused on weight changes, exclusively. In the exceptional studies that had both a sensible resistance training regimen and comprehensive analyses of body composition in place, on the other hand, suggest that the lack of benefits in the combined training analysis of Clark's study may be a statistical phenomenon.
References:

• Clark, James E. "Diet, exercise or diet with exercise: comparing the effectiveness of treatment options for weight-loss and changes in fitness for adults (18–65 years old) who are overfat, or obese; systematic review and meta-analysis." Journal of Diabetes & Metabolic Disorders 14.1 (2015): 31.
• Cuff, Darcye J., et al. "Effective exercise modality to reduce insulin resistance in women with type 2 diabetes." Diabetes care 26.11 (2003): 2977-2982.
• Donnelly, Joseph E., et al. "Effects of a very-low-calorie diet and physical-training regimens on body composition and resting metabolic rate in obese females." The American journal of clinical nutrition 54.1 (1991): 56-61.