I think check plays better here. First, I think he has a lot more 865/QJT/Q7 other random garbage than smaller backdoor flushes he can call with. Second this isn't a great river for your range. Obviously your nut hands stay the nuts, but all your middling hands would rather just see a showdown, and your bluffing range is super narrow. Since this hand is kind of in between a hand that wants to see a showdown and a hand that wants to get stacks in, I think it plays better as a check to balance out your check/folds. In other words, when you play bet/bet/check on this board runout in general, he's going to to be in an excellent situation to value bet very thinly, bluff very often, and only take/give free showdowns when both bluffing and value betting are completely nonsensical. Third, if you bet the river big, you're definitely over-repping your hand. Only better calls and all worse folds. If you bet small, his unknown value and bluff raising ranges present a problem. With your 2 pair blockers, you might have to bluff catch vs a raise, but 4's full do make up a reasonable percentage of his overall river range, so you have to play guessing games as to how often he raises his hands that can't win by calling vs. some goofy 1/2 half pot river sizing.