How to gain muscle mass using bodyweight exercises
The standard answer.... It isn't easy, and it's not very efficient.
IF....You are genetically gifted with a high percentage of fast-twitch muscle fiber in your makeup, and if you are willing to jump through the necessary hoops to continue to add resistance to your bodyweight exercises, you may see some improvement.
However.... In terms of attaining muscular hypertrophy, the simple fact is that nothing is as effective or as efficient as progressive resistance. (weights)
Consider...Pushups are a reasonable exercise for the chest, and there are many variations. But most folks will rapidly get to the point where they can do a LOT of them, at which point it just becomes an endurance exercise and you're not getting much stronger or bigger either.
You have to increase resistance. And with the pushup... This means having a partner put barbell plates on your back or something similar... Which means you're dealing with weights anyway.
The same with pull-ups... Even more so with squats and such.
You can certainly develop an attractive physique with bodyweight and calisthenic exercises. But it will not be the type of physique you can attain with weight training.