JJ what to do on the river

I believe this spots are opponent dependent. If he is aggressive, check call is usually ok.
However, from my experience at the lowest stakes, players are passive and will check more often, even with missed draws that dont have showdown value (on this board mostly flushdraws).
Ax has showdown value.
I dont mind betting. I have seen AK calling small river bets in this spots for instance.
They also wont bluff raise enough when you bet, which advocates betting. If you get called by better it is part of the game.

In my pool, hands like TT-77 are played as a call twice as often as a 3b preflop. That being said, they will be in his range often enough that I think we can block bet this river for like 30 to 35% pot and fold to a raise. Stack depth makes me think he will expand his 3b range, and the most logical expansion is to include TT here. He also has a bunch of missed AK, AQs here. These hands don't make a lot of sense to value bet against (are they ever calling?) but passive pools will also check them down sometimes since they do have showdown value. Folding out the cheese and not showing down (in a trackable environment) is a good thing.