Martial arts are like sport, even though some are not sport they share the EXACT SAME training principles. practice a skill enough and you'll get good at it but it wont necessarily make you stronger, it'll just make you better at that skill. the only way to get strong is to work against resistance. if you lift weights already then change your routine and try squats and pull overs 5x5. pull overs are great because they have direct application of strength into many movements of many martial arts e.g. the clinch in grappling or fok sao in wing chun.
Look into plyometrics, like clap hand push ups (clap not required). This could be usefull if your looking for explosiveness in chest/triceps. [ame="http://www.youtube.com/watch?v=mgkyTtQ0ODE"]Plyometric Push-ups - YouTube[/ame]
pop down to any ABA gym and see what practice, roadwork, practice and practie can do for a fighters skill. you'll also notice however they're pretty damn skinny, what're you doing WC for? to compete: do you have weight classes? for SD: what if a mugger is bigger or stronger than you? why the desire to avoid weights? i get some people dont enjoy them or whatever. hard to go wrong with pull ups and dips for the upper body. also gymnastic stuff is ubber cool but very tough. for lowerbody your going to struggle with BW only IMO.
Well I am starting to do some gymnastics exercises. I do a lot of situps and pushups and I run. I do lift weights but not all that often