He missed his first two years at Wisconsin with knee injuries.
Guys that struggle to put on weight (like Sean Lee) typically don't have the tendon strength to handle the additional muscle.
You can build muscle strength, but tendon strength doesn't really improve with it. No blood in there.
Knees get injured for lots of reasons. In Watt's case, they were ligament repairs for a floating kneecap. But there's a big difference between a guy who takes a helmet to the knee and a guy with soft tissue limitations.
I don't know enough about Watt's specific injury to have an informed opinion. What little I read about it sounded like it was a very specific problem that is initially treated with time off and then escalates to a surgical repair if necessary. It sounds like that's what they did. I haven't seen anything to suggest it's necessarily a significant re injury risk or anything to suggest he'd have an elevated risk if he put on weight.
I like Watt for us, but if I were to pick something to worry about, as I said earlier, I'd worry more about whether he could put on the weight legitimately first because Wisconsin does a good job with that already, and then about his relative inexperience early in his career than I would about the knees.