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I think there are more than just "monsters" being 3-bet out of BB. Especially from a tricky player. I think you're losing out by not raising this flop at a minimum. This is about as good a board as you're gonna see with AT. If you cant bet this hand in this situation, you should be folding this preflop to a 3-bet.

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I don't agree with this. There is a decent chance that we're ahead, as villian could have something like AK or AQ. But there is also a decent chance that villian has an overpair. So IMO the flop is VERY standard, raising the flop is bad, let him bluff off AK or AQ if he wants. The turn is where you could make for betting when checked to. But what do we do if we get check raised? Puts you to a tough decision and against a tricky player checking behind can be good.