back in the 50s they would have basketball players practice shots and passes with medicine balls...the theory being that it would make your shots and passes more powerful and all (and if you ever tried to take a half court shot [which you shouldn't really be doing much anyhow, other than if you only have a second left] you will know it does take some power). I am sure those throws did make guys stronger, but some of the first real application of sports science showed that you actually screw up your throwing mechanics using a medicine ball instead of a basketball for shots..hence you might get stronger but less accurate. A case where trying to be sports more specific is actually worse than the less sports specific alternative (like lifting or body weight exercise for improving strength..because those won't confuse your neuro muscle system for the throw).
I have never seen any studies on it..but i suspect it might be the same for boxing with weights. Now having said that...I use to do it all the time..and after i would do it for a few rounds I would go and shadow box without weights and "feel" much faster..but I suspect that was just a psychological illusion.
Anyhow...i would say some weights would be a good idea..but no more than whatever the gloves you will be wearing will weight...12 oz or whatever...
heck..good pros actually wear fight weight gloves in sparring (although usually the paid sparring partners still have to weigh 16 oz, I read that about Pac..i suspect it is for the reason above).
anyhow....paradoxically...i suspect medicine ball throws are good for boxing..because its far enough away from the boxing movement as to now really screw up the mechanics of the punch (but thats just me guessing).
Anyhow....just weight for dealt with....I am sure he will come in...make some comment about me being fat..and than tell you truth