[schwza]

pre-flop fine, flop fine, the turn check is no good. a very likely hand for villain is a flush draw, and he's drawing thin (maybe dead) so get him to call a small bet on the turn.

on the river, villain does not have A high. it's unlikely he's calling with A high on a 1/2 pot bet with two players still in the hand. however, there's a decent chance that he has a flush. villain is not going to call a push with a flush. he will probably call a pot-ish sized bet. so a pot-ish bet will get called a very high percentage of the time, and a push will get called every once in a while by 4x or 55-88. so i'd bet around 3/4 pot.