Stacks are right here? You're 240 BBs deep? I'm not wild about the no 3-bet, but you seem to know that already. As played, I'd lean towards just calling flop because your hand isn't really good enough to put in four bets and he'll value bet a lot of second best hands anyway if you are checking and calling. You can always bet river if turn checks through, or bet turn and river if flop checks through, so you're guaranteed to get at least two bets in even without check raising.

Once he three-bets flop it's a nasty spot (part of why I don't like check-raising, though it really shouldn't happen that much). There are exploitive reasons to think he wouldn't put in a big 3bet with trips+, but your hand is defintiely just a bluff-catcher, and if you don't have reason to think he's bluffing too much here, it's probably best to fold.