Check/call turn. I don't even think an A is in his range because I think he shoves bare overs instead of floating with them and shoves any that connected with that flop. He also shoves Adxd too.

With that figured out, I want to figure out the best way to get him to commit more chips with a small PP that he was perhaps waiting for the turn to make his decision for. If he's remotely aggro, he'll love that A as a bluffing opportunity. If he's not, then you leave the chance he might call your river bet because he thinks you're bluffing.

All in all, I see no benfits of firing the turn or even considering a fold at any point.