Weight training has limited effect until about 6 months after they reach their peak height growth velocity. They can get stronger up until then but it isn’t because the muscles are getting bigger. There’s also more risk while they are going through their growth spurt as my son found out when he ended up with a stress fracture in his back. Doing the wrong kind of lifts can exacerbate this particular problem. They are also at more risk for tendon and ligament damage due to the bones having grown faster than the muscles and weight lifting can add to that risk simply by increasing the amount of stress their muscles can bring to bear. At the same time that load can help develop the bones, tendons and ligaments if it is just below the level that would cause damage.
I’d recommend being very careful about using any significant amount of weight and being extremely careful that he’s closely supervised as to proper form at all times. Just teaching them the right form isn’t enough as kids will deviate from proper form to try to lift a bit more weight or for one more rep and will often end up injuring themselves.
Every kid is different and most can benefit from closely supervised, proper weight training but you need to be aware that there are risks, especially at your son’s age. Of the three baseball related spondylolysis cases in our area, two were relatively tall and thin and one was fairly stocky and athletic. Only my son was a pitcher. All three were involved in baseball conditioning programs going into their freshman seasons and had just turned 14yo. You can’t tell from their build who is at risk. We also had a case of a 14yo going on 15 damaging his pitching elbow by pulling away the growth plate. This probably didn’t have anything to do with lifting, but he was one of the hardest workers both on and off the field.