I know this is a topic where some people are strongly pro weighted balls and others feel equally strongly con. Lots of opinions to read out there but not much empirical evidence one way or the other on effectiveness (that I've found anyway).
I certainly have no evidence to offer, but FWIW... Soylent Grunt, 2016 RHP, did a program last year starting around this time which used weighted ball exercises along with other core movement exercises... A typical "velocity and mechanics" program run by a knowledgable instructor. Son's experience with it was along the lines of sore arm for first time ever, jacked up mechanics which resurfaced periodically over the summer, and in the end... About a 4 mph bump which I suspect was going to occur naturally regardless, given strength and height gains this last year.
That said, I am NOT contending that the velocity program necessarily caused any of the above issues. Son was nearly 6'3" and a thin 170 this time last year. Very possible that his body wasn't yet ready for what he was doing. He had a so-so Summer on the hill by his standards, but has been throwing the ball very well this Fall season... including a "sudden" uptick in velo. So who knows, maybe there were benefits to his doing the program a year ago... Maybe even overcoming some of that was a net plus? Who knows. Also, unlike the OP... son was certainly not working from 92 trying to gain more... that's a different situation entirely.
But for other parents of mere mortal rising juniors, I will say that... for us... If we had it to do over again, both son and I would opt to forgo the weighted balls and velocity program in general and concentrate instead on more traditional pitching and strength training methods. Just one experience.