Many people going to the gym lift heavy to get big, which is fine, but weight training for boxers and mixed martial artist needs to be a little different.
Lifting weights for a combat athlete needs to be explosive, so keep the weights light & due many reps. You want to simulate the movements & tempo of a fight, not only does this condition your muscles but it also gets your heart and lungs in fighting shape.
Weighted shadow boxing
Bent Over Row
Military press dumbbell & barbell
Squat & Push Press
Again, keep the weight light & the movements explosive. Make sure to use Proper Form, we are lifting to get stronger for the fight not to injure ourselves.