Check call.

His most likely holding is missed hearts, maybe with something a little extra (like a six, which is why bet folding is less than optimal. He could easily raise with trips here (I would)). He could also have some random ten, 109, 88, an overpair. All these hands would likely call $20, and might well check behind. I think it is very unlikely you are behind. I do not see many players waiting til the river with a set these days, and two pair with a six seems rather unlikely. Also 99 and 10-10 could very well raise preflop.

So, check call.