AT, turned trips but opponent is fighting back

[Bona]

If we put villain on a preflop 3-bet range of JJ+, AKo, and AKs.

The only hand in that range that beats us is QQ. There is a hand or three that beat us that aren't in that range but would he have 3 bet preflop w any of them?

There is at least a chance he might play AA, KK, JJ this way. I dunno know.

Anyway, considering that I think your 3 bet is not awful on the flop but once he caps we have to think we are toast. We probably should not have three bet just because of the cap possibility. Instead just call down from the check raise.

I think you have to be a better player than I am to fold anywhere but I'd be really surprised to win this pot or even to chop it.