AA vs 2b on flop and cbet turn

PokerStars - $0.02 NL FAST (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 100 BB (VPIP: 15.38, PFR: 12.31, 3Bet Preflop: 0.00, Hands: 67)
SB: 79 BB (VPIP: 25.00, PFR: 25.00, 3Bet Preflop: 0.00, Hands: 4)
BB: 106.5 BB (VPIP: 31.71, PFR: 19.51, 3Bet Preflop: 0.00, Hands: 41)
UTG: 82.5 BB
Hero (MP): 180 BB
CO: 374.5 BB (VPIP: 28.57, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 21)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has A♣ A♠

fold, Hero raises to 3 BB, fold, BTN calls 3 BB, fold, BB calls 2 BB

Flop: (9.5 BB, 3 players) Q♥ J♣ 3♥
BB checks, Hero bets 6.5 BB, BTN raises to 13 BB, fold, Hero calls 6.5 BB

Turn: (35.5 BB, 2 players) 9♣
Hero checks, BTN bets 27 BB,

Hero?

The 9♣: completes KT which now also beats me in addition to flopped sets or 2pair. Is a fold mandatory? I am not sure if he has QQ or JJ because he might 3bet pre. He might still have some draws, too, especially hearts, since I am blocking nut club draw...