Hello JHTAN,
Well, against that kind of opponent who definitely has even Qx hands in his range, I don't mind to Bet/Fold. Although while there couple of draws even completed I doubt that he will ever bet with worse anyways, so you can as well just Check/Fold. According his play-style it might be even the case that he ain't paying with just Qx here on such a board.
Best Regards.