When it comes to weight training for boxing, no other single exercise has made as much of a noticeable difference in my boxing as heavy squats. When I first started boxing I had come from years of weight training and had a decent amount of size and strength. Unfortunately for my height at 5'7 "weighing 177lbs was not going to put me in an advantageous position to win fights. push-ups, burpees, ab work, and of course boxing itself. It took me about 4 months to slowly get to my desired weight, by the time I was there I felt great and really light. had sharpened my technique, my power on a single shot had taken a serious nosedive. I remember at first really being able to move guys back with the jab, and I could throw a right hook to the body that would echo through the gym. did not worry about it too much at the time, my skills had gotten better and I thought that losing power was just a natural part of dropping weight and being more precise with technique.
It was not until I went to the gym with a buddy one day about 2 years later that I re-introduced myself to squats and deadlifts. I could not believe how weak I had become, it was a hit to the ego that my strength had practically cut in half. I made it my mission to get my strength back in the hydraulic lifts (squat, deadlift, and bench press). After about a 6 weeks of steady work most of my strength started to come back, particularly in the squat where I used to be able to do 4-6 reps at 315lbs (3 plates on each side).
I sparred later that weak to prep a guy for the upcoming Provincials, and after the second round the coach came around to my side of the ring and whispered to me, "hey take it easy, he says you're hitting too hard." What !? I laughed to myself, I'm hitting too hard !? I had not heard that in a long time, and especially from a guy at this level. But he was on to something, I noticed I was not getting pushed around as much in the ring, I could hold my stance, block shots and then throw with more solid balance. It also became easy and natural to lower my levels to get under shots and rip to the body. I found myself transitioning and stopping and starting with relative ease. Essentially my legs were carrying me around like it was nothing. I had not felt this solid since I started, but now I had a full arsenal of techniques to go with my new found strength.
There's always the question of whether weight training slows you down, my belief is that it does not and can in fact speed you up. However, adding too much weight can slow you down unexpectedly and it takes more work on the part of the heart and lungs to support that weight. My advice to you from practical experience is to take squats seriously and build up as much strength and power as you can in this exercise. Watch how much more solid and agile you become in the ring.