Re: 4.40 with barely an overpair..
I think he probably checks turn with a 6. But he's not that likely to have a 6 anyway (he was pre-flop raiser). Preflop let's put him on most likely having two broadway or a pocket pair.
He's either leading or check-raising an overpair, so check/call points to him floating with overcards.
His turn bet could either be pairing a Q or just a feeler to see how strong you are. Since you don't raise the turn, he probably can safely assume you don't have a Q. That being said, I wouldn't raise the turn either. I'd call and hope for a cheap showdown.
At that point, his river push seems like it could be QT/QJ/QK feeling safe he's not up against a better Q, or it could be a pure play (discounting the few times it's a 5 looking to get paid). Unless I have evidence indicating that villian is capable or making such a bluff, I'd give credit for a Q and fold.
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