i think if villain have AA he will not bet flop, like you, if he have almost the nuts, he want to trap you.
i think villain can have AJ+ JJ+ KQ(if loose)
For me, easy call. what he had?
GL

You beat everything except AA and 66 - can never fold - if it is AA or 66 then suck it up

maybe 4 bet preflop might need to be considered

Not sure how often villain 3-bet bluffs preflop, but he could also have hands like 108s, 54s, 67s, 68s. If hes aggressive hands like KK, AKo with a spade perhaps. Hand is too strong to fold.

Must call spot. If you don't make this call you're super, super exploitable. If it's AA or 66 it's a huge cooler and it is your time to go. I expect him to have a lot more overplayed AK here than AA or 66. He can also have AKs or KKs so much stuff he can have here that you're crushing. He may even have something like K4s that 3bet light if he's a decent reg and thinks he's shoving for value with the nut flush.