ok, second attempt to answer this – first one got dumped. 

What is villains range? given that he has just flatted the BTN pre, his range can be capped i.e. it is v unlikely that he has AA but not impossible, equally it is unlikely he has AK but not impossilble as people do flat both of these with a small frequency. Other possible holdings are 55 and 22 that might take this line on the turn, equally 34suited is the nuts in this hand and 2 combos can river a flush. 3,4 is a possible holding but I would give it a reduced likely hood. It is also possible he is on a semi bluff here with something like KsJs e.g. he repp’d the Ace on the flop because you checked to him then picked up a flush draw on the turn, when you check called the flop it is most likely you have either a weal Ace or an underpair, to get you off either on the turn he bets big, at the same time this builds a pot it you get stubborn and call again and he hits river. 

Now, against the above you are only crushed by AA (which he only shows up with a small portion of the time), you are a dog to 3,4 but have a good amount of outs, and way ahead of everything else. I am weighting him more towards 55, 22, AT-AQ, and semi-bluffs all of which we crush. I am raising on the turn to get max value from these hands right now, as there a a bunch of river cards that will shut down the action. I would be willing to go with it as well if he puts us all-in (which he would with 55 and 22), if he shows up with AA or 34 so be it and good game.