I don't like 3-betting the flop here either. I like your lead out on the turn as well. I think check-calling the turn and leading out the river is a decent option too, but you run the risk of him checking the turn as well. If you put him on a big ace though it's not likely he would check the turn. I agree with you that he is probably checking behind on the river if you give him the chance. Overall I think you played the hand very nicely.