You set yourself up for a river shove, and I don't think the villain will check a big hand on the river with $10.95 left and a $30.25 pot. It just doesn't make sense. I say shove here since you'll be laying the villain 4:1 to his money and the betting is consistent with QQ, a big J, or KQhh here. All of those hands may pay you off when you're giving him 4:1 odds.

I usually like to try to keep pots small on wet boards with aces, so I might check the turn here for pot control. I don't like committing myself to a river shove if a flush or straight card comes, but maybe that's just me being too conservative.

As played, however, I shove the river.