What range does villain hold that cold calls this flop and check-raises the turn?

Would a range of {77,33,AsKs,KsQs,6s5s,5s4s} be acceptable (6s5s is pushing it a bit imo)? We are behind villain's range.

I don't see many villains playing their draws too aggressively and given possible combos...I give the possible sets more weight. How is this an easy shove?

I like the idea of bet/folding the turn. We are ahead of villain's calling range and way behind his raising range. Am I missing something here?