Building muscle does not burn all that many calories. Weight lifting burns a lot of calories with the combined effects of the energy expenditure while training, and the heightened calorie burn after the session from the anaerobic work.
Losing weight should be your first priority. Part of the process of losing weight should consist of a solid nutritional strategy, cardio, and resistance training.
The resistance training is not thrown into the mix so you build muscle. Because guess what. You can't build muscle while you are in a calorie deficit. And if you are trying to lose weight, you MUST be in a calorie deficit.
Weight training is thrown into the mix for an added form of activity that burns calories and more importantly, for muscle maintenance. A caloric deficit will always lead to a loss of tissue, which consists of both muscle and fat. By having weight training as part of your program, it allows the tissue loss to stay more toward the fat side of things, opposed to the muscle side.
To build muscle, as a few of the posts elude to above, you must be in a caloric surplus. Muscle is an energy expensive tissue, and building new muscle on top of what you already have is an even more expensive process, energetically speaking. To support that kind of growth, you need to be eating above maintenance.
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