[William]

When you raise with QQ and are called, what are you hoping for? To hit a Q of course, but the very next best is a flop with undercards. That is what you got here, so you should be happy. If you check, the free card could be an overcard, a third heart, a small card that hits his small PP (if he has one) Even if he has completely missed the flop, he could sense fear in you and move in. You're probably going to call anyway, so no need to give the free card.
i don't think you have to fear AA or KK. He would probably have made it clear pre-flop. And if he has a J, bad luck, you need a certified cristal ball to come alive from the situation anyway.
Remember there are only 2 J's left and no hand including a J would normally call your pre-flop raise (except JJ of course). You have got the flop you were hoping for, act on it.
Holding AA, my play would be just the same.

Take care,
William