Villain was 26/16/5 (3bet) through 74 hands. Fold to cbet, 50%, 2/4.

PokerStars - $0.05 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BB: $4.00
UTG: $5.00
MP: $11.41
Hero (CO): $7.52
BTN: $10.04
SB: $3.40

SB posts SB $0.02, BB posts BB $0.05

Pre Flop: (pot: $0.07) Hero has K K

fold, fold, Hero raises to $0.15, BTN raises to $0.45, fold, fold, Hero raises to $1.05, BTN calls $0.60

Flop: ($2.17, 2 players) 8 A J
Hero bets $1.55

Should I be leading out on this flop? I was trying to think of hands that I beat in villain's 3bet/4bet calling range. All I could think of was QQ & TT. KQs maybe, although KsQs calls I feel. AJ+ has me crushed, JJ has me crushed, obv AA had me crushed pre.

On the other hand, by checking, am I playing my hand face up? Allowing villain to bluff me if he thinks the A has scared me?

Thoughts on correct play?