I'm beat but I can outplay him postflop... or can I

[UprightCreature]

NL game, stakes don't matter. Villain is selective preflop and very LAG post flop. In fact villain will go all in no matter what on the flop.

Hero is in the cutoff and villain is on the button. It doesn't really matter what the exact action is except that hero has 9Ts and has entered the pot. Villain makes a pot (X) sized raise and all fold back to hero.

Villain’s range here is AA-TT,AKs-AJs,AKo-AQo,KQs

Hero has to call X more making the total pot 3X. How deep does the smaller of the two stacks need to be for this to be a profitable call? How about if the Villain made a double pot raise (2X)?