Villain can have some AA/KK, but I think that Jx-hands are a bit more likely (AJ/KJ type of stuff that he bluffed with preflop). I also don't want to give free cards to AK which is a pretty decent part of his range. Some A5s kind of stuff is also possible, I don't mind him folding that either.

I would have folded if he check/shoved since I have a heart in my hand that blocks some of his flushdraws. It would be closer if I didn't have a heart. I think flushdraws are more likely to check/shove than AA/KK, and villain should not have hands like 99/JJ given that we're deep and he 4betted preflop. What would you do with QQ without a heart if he check/shoves?

Biggest question is my river play. Did I miss value by checking back, what do you think? I was kind of scared of AA/KK that he might have occasionally, but villain can also have stuff like AJ/KJ/JT, and my range contains decent amount of floats like AK/AQ, mainly with a heart. I also beat JT/J9/T9 type of hands that are pretty tempting bluffcatching hands for him given those floats in my range and the fact that he blocks my sets.

Villain has 51 dollars behind.