I don't think this villain has a backdoor draw too often, but that is just based on pf stats, so take that FWIW. I guess it could be Ahxh/QhTh, but that is about it.

If you check, AQ/AK could check behind as there is not a lot that they are beating and the board is getting pretty scary. A9 may still bet, but why give him the chance to check behind. Busted draws may or may not bet. With your read that he doesn't have a set, the call seems pretty straightforward.