There are a few different goals that most weight lifters are shooting for: hypertrophy (size/mass gains), maximum strength, muscular endurance, and finally, explosive power. Some hypertrophy or gains in mass are bound to happen if you lift weights, but the gains in size can be insignificant in comparison to the maximal strength and explosive power gains IF you train properly with those goals in mind.

Typically speaking, 8-12 reps per set with a slow tempo will produce the best gains in size. So if you want to be a boxer, avoid that training style. If you want to build muscular endurance, you may want to try using light weights and doing as many reps as possible in 60 seconds. Or you may want to build explosive power in which case Olympic style lifting might be a good option. Or just use a moderately heavy weight but complete each rep as quickly as possible. Or you may want to train for maximal strength, in which case you want to train with very heavy loads and very few reps. If you train for maximal strength, you'll need to dedicate a significant amount of time to plyometrics and speed training to ensure you don't lose speed.

In the end... Weight Training should be a part of your training, but you need to ensure that you're doing it properly with the right goals. Bodybuilders are rarely fast, flexible, or mobile enough to make the transition into combat sports. Olympic lifters are a whole different story because they train for explosive power and most have excellent flexibility and mobility.