Annoying spot with AK 270bb deep

Villain is 30/25/9 in 700ish hands.
What should I do on the turn? I basically discard bluffs. He went huge 3/4 3/4 Flop and Turn.
IMO Villain is weighted heavily towards AA with a little QQ, KK, AK
My hand is so strong tho, can I ever fold or meh jam? Or call and fold if unimproved or call/call.

Yatahay Network - $0.25 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 748.52 BB
Hero (SB): 269.6 BB
BB: 106.32 BB
UTG: 100 BB
MP: 100 BB
CO: 198.48 BB

Hero posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has A♦ K♦

fold, fold, fold, BTN raises to 2.8 BB, Hero raises to 11 BB, fold, BTN raises to 26 BB, Hero calls 15 BB

Flop: (53 BB, 2 players) 5♥ 7♦ Q♦
Hero checks, BTN bets 32.32 BB, Hero calls 32.32 BB

Turn: (117.64 BB, 2 players) K♥
Hero checks, BTN bets 83.6 BB