Actually, that was the first thing I thought, and two clubs was the second (though the fact that you posted a thread made me assume it was something byfuglien).
For one thing, Ax is not a strong LAG hand. Granted, we don't know for sure this guy is a good LAG, but LAGs don't want hands that only hit when TAGs will hit harder. They want hands they can hit when TAGs miss, or hands they can hit harder when TAGs hit, and Ax fits neither description.
This is such an ugly spot to be in post-flop. He's an aggressive player who has re-raised the flop and cold-called the turn on a scare card. This means one of two things: The scare card hit him or it scared him, but not enough to fold a hand.
What does that mean? It means his range is slow-played flush, set, straight, AQ, weaker 2-pair, AK/AJ, naked bluff. Your hand behind a large chunk of his likely range on the turn, but it's probably too good to fold.
I think there's a strong case to be made for a softer play on the river here. Checking gives the chance for him to check behind on the hands that beat you but don't beat the flush (sets and straights) and if he's got the flush or he's behind you, he likely makes a value bet that you can feel comfortable calling. If he shoves into this board on a bluff, good for him, you have to fold and you'll get him back later when you do have the flush.