I like the way you played that hand and i agree with datsmanahme that i'm also just calling 100% against 3bets unless villain is a fish but with just calling you keep your range wide, you can bluffcheckraise more on the flop because you've more stronger madehands and AT is actually not a hand you necessarily wanna be playing with initiative oop. I mean it's ok to cap but competent Opponents will recognize when you have 2 ranges. a cappingrange with just the premiumhands and a callingrange. You are easier to play but just wanted to mention it though i know that you already know. 
Board:
Equity Win Tie
MP2 44.87% 41.73% 3.14% { 44+, A2s+, K8s+, Q8s+, J8s+, T8s+, 98s, 87s, 76s, A5o+, K9o+, QTo+, JTo }
MP3 55.13% 52.00% 3.14% { ATo }
We've just a marginal advantage against a loose 3betting-Range and the edge gets thinner the tighter his range becomes and in reality it'll probably a bit tighter as assumed in this calculation.
Not having initiative you can play more according to your eQ and you don't have to autofire the turn with less than 50%, if you don't hit, . The positional disadvantage of being oop is still a lot underestimated.
The question is actually not whether you should cap the flop or not i guess. Call 3bet is quite standard since your kicker ain't that strong and you balance your bluffs and flushdraws that way.
River i'd got for a bet as well because he seems to have some weak pair he's certainly paying off with. You could argue: He's certainly on a mid pocketpair and wouldn't he be more inclined to check back the turn with a flushdraw and thus bet the river as well. Without a flushdraw he would be more inclined to bet / fold but a guy who plays that "strange" line doesn't think that way. So he could still have too many random pairs without a flush that he's going to pay with so without a read i don't like checkraising.