he should never check back 33 or 44 or 9x on the turn. He should almost always 3 bet JJ pre so river raising by villain is very strange to see (should basically never happen here). If you have a read that he doesnt bluff there I guess its fine to fold but GTO-wise you gotta call for sure.

I agree with zinom but would add that even if villain basically never bluffs, we probably still have equity against his merged value hands (worse 9x such as 98, 97). We are dealing with a narrow range so just having a few combos of merged value we beat is probably good enough on it's own to merit a call. I also agree that those hands shouldn't be checking back turn, but also, this line basically doesn't make any sense with any combo of hand in the deck. Fish do weird stuff and it's possible for this player to have some merged value here.

EDIT: I am curious why OP chose to check turn here. Why not barrel for value?

38/27 will ever Xb there 9x .33,44 ? I dont think so . This line looks strange , i'm not folding . JJ 3bets a lot but if not he propably bets some % of this on turn . I call .