no real reads, seen 12 hands with villian, 3 hands earlier he raised 3xBB, I re-raised 9xBB with QQ and he folded

PokerStars No-Limit Hold'em, $0.50 BB (9 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

saw flop|saw showdown

Hero ($54.30)
SB ($13.35)
BB ($50.45)
UTG ($34.85)
UTG+1 ($36.75)
MP1 ($48.35)
MP2 ($56.20)
MP3 ($29.70)
CO ($52.80)

Preflop: Hero is Button with K, K.
2 folds, MP1 calls $0.50, 2 folds, CO calls $0.50, Hero raises to $2.5, 2 folds, MP1 calls $2, CO folds.

Flop: ($6.25) Q, K, J (2 players)
MP1 checks, Hero bets $4, MP1 raises to $9, Hero calls $5.

Turn: ($24.25) 6 (2 players)
MP1 bets $9.5, Hero raises to $20, MP1 raises to $36.85, Hero ?

What do you think, does he have AK, QQ, JJ, QK, QJ or the dreaded AT?