Why raise to 4000? Vilain raise to 3xBB and you only raise to 6.5 BB. Wouldn't a raise to 5000 be bettor to get more info?

I think that folding is tight but not necessary wrong. Playing back at him for a 3rd time could make him play back at you, you don't want to call a re-raise neither loose 4k.

So call can be an option, but if the flop is low, and you call a bet of let's say 3000. The turn is low again, can you really fold to a 7000 bet that commits you? I think that not risking it, when you don't feel you'll have control of the hand is the right move.

I'm not afraid of playing on the flop, but I'm not willing to give that much of my stack when I'll have a hard time playing the hand.

Would you call with AJ?