Villain is a decent TAG 200/400NL regular. Besides having played with each other before i have been aggressive at this table, so it's possible he could call my 4bet with J-J/Q-Q. With A-K i assume he would go all in preflop.

Is bet/fold, check/fold, or bet/call the best option?

PokerStars No-Limit Hold'em, $2 BB (4 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

SB ($102.30)
BB ($240)
UTG ($243.15)
Hero ($197)

Preflop: Hero is Button with K, K.
1 fold, Hero raises to $6, 1 fold, BB raises to $22, Hero raises to $54, BB calls $32.

Flop: ($109) A, 4, 4 (2 players)
BB checks, Hero ?