Facing Turn Shove Against Unknown

I was put into a tricky spot vs an unknown player on a deep table.

I'm guessing that I will get a range of answers here. What would you do in this situation?

He raises and I 3bet my button with a sexy looking suited hand.

Take a look at the graphic.

For some reason there are no stats on him (reason to come in follow up post).

He leads the flop in a spot where I have decent equity:

I have a potential double gutter and back door flush too. I could raise here but if he has a set and shoves I don't really want to call with only around 35% chance in a deep pot. This is an excellent spot to float.

The turn is an awesome card and I hit my straight.

Then..... Bang....

I am faced with a huge shove which is 3x the pot due to the fact that we are deep and started the hand with 200BB effective. 

Does he not 3bet his AK pre for value vs a button raise that could be wide? Or would he just call with AK OOP because we are deep and he is not aggro? I can beat 89 which makes sense with the flop donk bet. Does he ever do this with a set or less? Surly this is AKhh and nothing else?

What do I do?