Bodyweight exercise is good up to a point but if you want to add muscle mass you will need to lift heavy.
Problem is it's difficult to lose fat and gain muscle at the same time. One needs a calorie deficit and the other needs a calorie surplus.
If you lose weight too quickly without resistance exercise you will likely lose some muscle as well as fat. That is why it's best to aim for a modest rate of fat burn of half a pound to a pound per week. People with a lot to lose can usually lose at a higher rate at first.
DJS makes a very important point when he says you can't "spot lose." Your genes will decide which fat cells it burns first. Everybody carries their fat differently.
There are so many myths about nutrition and exercise.