[teteatot]

I think how you describe villain makes your flop play fine, but your turn play bad. You've said he won't value bet his big hands enough, so why not just c/c the turn and bet a blank river if he checked turn, unless you think he'd bluff a busted draw, in which case c/c again. I think the chips you lose from letting a flush draw get there is less of a factor than chips you save from not going broke if he has a big queen or hit another 4.

Without that read, this spot would be a lot tougher, and too opponent specific to say what to do.