If you are still here aaa123 (and I fear we may have lost him), I would like to add that as has been noted by several posters, using weights requires adjusting the amount to the needs of your ability for the particular lift. To do that you need a set of dumbbells or an adjustable type. Body weight exercises can be progressive without that investment by varying the exact sort of body weight exercise. Get up to over 20 push ups in a set? Do some plyometric ones (push up explosively enough to be able to clap between push ups), or offset to one arm doing more of the work aiming to doing one arm ones, or incline, or hand stand push ups, or, best yet, mix up between them. Get up to over 20 pull ups? Also do some asymmetric ones working towards being able to do the one arm, or work towards doing muscle ups (please note, I have doing some of those as unmet personal goals!) Many of the best and most serious training programs around currently include body weight exercises as part of their mix - along with the weight training and high intensity aerobics.
Hershel Walker’s body weight only program has already been alluded to - and here’s a link that includes a photo of him. I doubt too many vanity exercisers would be disappointed with that physique. Nor would many be upset to have the arms of a male gymnast.