My experience seems to show that you can't significantly change
anything regarding your physique with solely your body weight, even if
you work out regularly for years. On the other hand, you can find
loads of shredded YouTube individuals arguing that you can build your
muscles effectively with nothing but your body weight.
Where's the truth?
If you search around a lot of the questions on here (and other fitness related communities), you'll constantly find individuals asking essentially the same question, but instead of bodyweight; they're asking why using weights doesn't work for them, why machines don't seem to be working for them, or, my personal favourite, if everyone with a semi-decent physique is on gear.
Yes, you can change your physique with solely your bodyweight. Or you can use weights. Or machines. Or you pick up a new born calf and carry it every day for several years as it grows into a cow.
Any sort of physique change is hard. Your body doesn't want to change, it's happy how it is, you need to convince it of the NEED to change, you need to convince it that a physical adaptation is necessary for survival.
If you're constantly loading a heavy weight across your shoulders and squatting with it, lifting a heavy load from the floor, or pressing a heavy load overhead, your body will respond. This is why powerlifters / strongmen / weightlifters gain muscle.
Likewise, if you're constantly challenging your body through various movements of increasing difficulty, front levers, planche push ups, one arm press ups, one arm pull ups, your body will response. This is why gymnasts have impressive physiques.
I guess some would say something like, "Yeah, it's not about weights,
it's about progression, so you can do two-arm pushups, then one-arm
pushups" — okay, and then what? Levitate?
Yes and no. Yes, progressions will get you stronger, a one arm push up or pull up is an impressive feat of strength, but if your goal is to build an appreciable amount of muscle, then you also have to stress the muscles with sets of higher reps.
If you can already perform 30 press ups non-stop, then you're going to be hitting a point of diminishing returns as far as muscle building goes. You would be much better served picking a harder push up variation (requiring more strength) and working on that until you can do a decent amount of reps, then pick a harder variation, and so on and so forth.
I wouldn't recommend levitation as a progression for press ups. Whilst undoubtedly impressive, I feel that removing stress from the muscles you're trying to work would be a little counterproductive.
Is there a real possibility to turn yourself into, say, Brad Pitt from Fight Club (not Schwarzenegger from Mr. Universe but pretty toned) without any shortcuts like weights and chemicals (supplements)?
No, for the simple reason you're not Brad Pitt, and you don't have his genetics. Yes, you can build an impressive physique with purely bodyweight exercises, but you do have to work hard for it (like you do if you take a "shortcut" with weights).
The only caveat I would throw in is that while you can almost always find a progression for upper body work (I've yet to see anyone who can knock out a set of 10 one arm handstand press ups), when it comes to lower body work, you might find that you do need to add additional weight after a certain point.
All of this presupposes that you're sufficiently handling your recovery. If you're not taking care of your nutrition, sleep, stress levels, water intake, etc, etc, then it doesn't matter if you're doing calisthenics, weight lifting, or carrying the aforementioned bovine creature, you'll find it very hard, if not impossible, to significantly change anything regarding your physique.