Everybody has their own preferences.
Personally I like bodyweight exercises because they're convienent and you don't need much equipment. Plus, you can change angles and employ static holds to make them much more challenging, and they're great for training explosive strength and muscle endurance, which is critical for fighters.
Old time fighters steered clear of weights and focused on bodyweight movements, but the new breed employs more weights while saying that the old-timers aversion to weights is unfounded.
But for some reason, something tells me that the old-timers weren't as clueless about weight training as today's weight training proponents would have you believe.
After all, weight training has been around for a long time. Squats, deads, benches, and oly lifts aren't anything new, and I'd wager that the old-timers tried all of them before concluding that bodyweight movements were the best way to go.
Guys like Marciano, Frazier, and Tyson before he went to prison, to name a very few, didn't use weights, and could punch a hole in your head.
Hard work beats talent when talent doesn't work hard.