AK gets there on river after reraise and 2-barreling, still kinda deep

[DJ Sensei]

10/20 fullring, but might be like 6 handed or something. whatever.

Button (18/10, always bets pot if he bets, seems overly straightforward when sober and HORRIBLE when drunk, but he's sober now i think) opens to 90, I repop to 280 wiht AK from SB, he calls. we're 4k deep too.

Flop 933r, I bet 390 into 570, he thinks a little and calls.

turn Q, i bet 880 into 1350, he thinks again and calls.

river A. We've got 3k each left in a 3k pot, or close to it.

-bet or check?
-how much?
-do i fold to a raise?

i'll post my actual action later, but i'm curious to hear what yall would do first.