I believe that they work, but I have no empirical data to support that opinion. On the other hand, my son gained 11 mph in 6 months (56 mph to 67)using weighted balls and a pitching-specific workout regimen as a 13 yo. He also gained another 13 mph in the following year. Granted, he was growing taller and stronger at the same time. This year, he didn't work with the same coach and gained (maybe) 2-5 mph just working pens, with no pitching-specific workouts or weighted ball training.
As to any theory being "true", if it was proven either way it would be a fact, not a theory :lol: Apocryphal accounts like the above are interesting, but remember, your mileage may vary. It's what makes sense to you. Personally, I was concerned that throwing a 9 oz. ball would create problems with his release point and change his arm action to compensate for the extra weight, but with the coach there to help him maintain his mechanics, it didn't hurt him at all. The trouble occurs when the pitcher compensates, trying to throw strikes with the heavy ball, and changes his mechanics.
I am going to work with him myself this off season using the same workout program that his previous pitching coach was using in hopes of helping him gain more velocity and stamina to go deeper in the game throwing harder. Right now as a 15 yo he is cruising at 80mph and touching 83 on occasion and was gunned at 81 in the 6th inning of one game this year. His pitching coach is going to concentrate on off-speed stuff this winter, and my son wants to develop a cutter/sinker combo that he can set up with his 4-seamer.