his range to check call the flop is like Ax ... all of which beat you besides A3 or whatever, and a FD. the FD gets there on the turn, what are you actually beating now? a bet doesn't get value from anything, so check behind on the turn unless u want to try to bluff him off of a stronger ace ... but in a lot of cases he's gonna have like AT w/ Th or whatever and won't be folding it cuz he probly figures he has the best hand or the best draw. there really is no 2nd best option, only option is to c/b turn and fold to a river bet.