My recommendation to use weighted baseballs (4 oz., 5 oz., and 6 oz.) comes only from personal experience -- I used them and they worked for me and my pitching. The weighted ball program I used is available on my Web site.
Funny thing was, I didn't research weighted baseballs before I used them. A friend of my dad's, who was a college coach, simply gave us the two weighted balls -- 4 oz. and 6 oz. -- and my dad and I used them each off-season throughout college and pro ball.
It was really no big deal then, and I think it's no big deal now.
Now I know that weighted baseballs are looked at differently today -- there's a lot of uncertainty and concern surrounding their use. I fully understand, too. If you don't have good mechanics, you may have an increased risk of injury because the 6 oz. ball, for example, is 20% heavier than a normal 5 oz. baseball, which presumably means there's more stress on the arm.
However, I had very good pitching mechanics, so that never factored into a concern for my dad or me.
Last year I began to research the topic a little because one instructor, who has a popular pitching Web site, was writing articles, which were 100% against weighted baseballs and 100% opposite of my own good experience with them.
In my findings, I came across some studies in a couple of different scientific journals that showed use of weighted baseballs (not exceeding 6 oz. and not less than 4 oz.) were just fine, and both showed that they actually promoted pitching velocity similarly to overload/under load weight room training.
Bottom line: For me, personal experience wins. I like weighted baseballs in the off-season. The key for me was to use them AFTER I had been throwing for about 3 to 4 weeks so that there was a good "throwing base" already established. I used them for about two months. Then, I cut off use once the season got underway, and I focused on fine-tuning accuracy and off-speed pitches.