The truth is it is extremely hard to build muscle and lose weight at the same time. It can be done, but at a very slow process. More likely you should focus on eating a well balanced diet while stripping weight (1-2 pounds per week), meaning fat and muscle, then building 2-4 pounds of lean mass per month once you achieve your target fat mass percentage.
As we can see from Tom Burn’s results, there is a correlation or relationship between fat loss and muscle gain. Various studies have shown the relation between fat free mass loss and muscle gain among different groups during exercise. Here are several of them below:
Given that resting metabolic rate (RMR) is related largely to the amount of fat-free mass (FFM), the hypothesis of this study was that strength training, which stimulates muscle hypertrophy, would help preserve both FFM and RMR during dieting. The strength-training group, however, lost significantly less FFM (P < 0.05) than the aerobic and diet-only groups. The strength-training group also showed significant increases (P < 0.05) in anthropometrically measured flexed arm muscle mass and grip strength. Mean RMR declined significantly, without differing among groups. Peak oxygen consumption increased the most for the aerobic group (P = 0.03). In conclusion, strength training significantly reduced the loss of FFM during dieting but did not prevent the decline in RMR.
Another meta-analysis was performed to assess the effects of type, duration and frequency of exercise training on changes in body mass (BM), fat mass (FM), fat-free mass (FFM) and percent body fat (percent fat) both for adult males and females. Weight loss following aerobic type exercise training, though modest, was greater for males. Stepwise regression suggests that, both for males and females, energy expended during exercise and initial body fat levels (or body mass) account for most of the variance associated with changes in BM, FM and percent fat associated with aerobic-type exercise training. In females, weeks of training and duration of exercise per session were also significant predictors. These findings confirm earlier research in males concerning exercise training effects on body mass and body composition and extend them both to females and to a broader range of exercise types. Of particular interest in this regard is the finding that weight training exercise which is similar to aerobic exercise in facilitating body fat loss, can also preserve or increase fat-free mass.
Another study proposed that muscle dysfunction and associated mobility impairment, common among the frail elderly, increase the risk of falls, fractures, and functional dependency. They sought to characterize the muscle weakness of the very old and its reversibility through strength training, and concluded that high-resistance weight training leads to significant gains in muscle strength, size, and functional mobility among frail residents of nursing homes up to 96 years of age. Good to know for the body composition needs in older populations
The purpose of this last study was to compare the effects of single- and multiple-set strength training on hypertrophy and strength gains in untrained men. The results demonstrate that 3-set strength training is superior to 1-set strength training with regard to strength and muscle mass gains in the leg muscles, while no difference exists between 1- and 3-set training in upper-body muscles in untrained men.
Rønnestad, B. R., Egeland, W., Kvamme, N. H., Refsnes, P. E., Kadi, F., & Raastad, T. (2007). Dissimilar effects of one-and three-set strength training on strength and muscle mass gains in upper and lower body in untrained subjects. The Journal of Strength & Conditioning Research, 21(1), 157-163.
Geliebter, A., Maher, M. M., Gerace, L., Gutin, B., Heymsfield, S. B., & Hashim, S. A. (1997). Effects of strength or aerobic training on body composition, resting metabolic rate, and peak oxygen consumption in obese dieting subjects. The American journal of clinical nutrition, 66(3), 557-563.
Fiatarone, M. A., Marks, E. C., Ryan, N. D., Meredith, C. N., Lipsitz, L. A., & Evans, W. J. (1990). High-intensity strength training in nonagenarians: effects on skeletal muscle. Jama, 263(22), 3029-3034.
Ballor, D. L., & Keesey, R. E. (1991). A meta-analysis of the factors affecting exercise-induced changes in body mass, fat mass and fat-free mass in males and females. International journal of obesity, 15(11), 717-726.