[Nohage]

When the button calls the flop I would put him a draw like 100%. I would toss AAragrag quickly here in his position. Furthermore, just because he 3bets pf, that shouldn't necessarily mean he has a high pair. With deep stacks it's better to 3bet good drawing hands than high pairs. That said, I would play it very slowly when the turn hits, because that is that card means the most likely draw for the button has hit. I would check and re-evaluate, probably c-f.

EDIT: I have assumed you're playing thinking opponents, if these live games are full of donkeys it makes things different ofc. However, I would still put BTN on a straight a lot so check turn.