You have a strong hand, 2 over + flush draw.

Would Vilain re-raise with AJ, nope. so Vilain may have AA -10-10. Or AK/AQ. I would do a check raise (making it clear that my stack goes all-in on the turn whatever comes) to take it down on the flop. If he checks behind, he doesn't have AA-JJ and probably not AK or AQ, so you get a free card and know that he may have a mid-pocket pair or he missplayed JJ. I would lead the turn (pot size bet) if checked behind.