BB - 19/17/5 (3bet) over 576 hands. Folds blinds 88% of time, fold to 3bet 82%, fold to cbet 47%. Breakeven player.

CO - 15/14/0 (3bet) over 70 hands, folded to only 3bet so far.

Had seen villain call 4bets on two separate occasions with KK and AA, OOP and IP respectively. He c/r AI with KK on paired flop, played his AA a little slower, calling flop and then calling turn shove.
Villain had raised flop cbet with overpair or less and no draw and played his draws agg.

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

Hero (BTN): $8.00
SB: $2.58
BB: $12.69
UTG: $3.03
MP: $5.43
CO: $5.89

SB posts SB $0.02, BB posts BB $0.05

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

fold, fold, CO raises to $0.15, Hero raises to $0.50, fold, BB calls $0.45, fold

Flop: ($1.17, 2 players) Q 7 A
BB checks, Hero bets $0.55, BB calls $0.55

Turn: ($2.27, 2 players) 9
BB checks, Hero bets $1.45, BB calls $1.45

River: ($5.17, 2 players) 4
BB checks, Hero checks

OK, so villain just decides to call pre. I had seen him do this with 4bets holding KK/AA so didn't narrow his range too much.

I thought I was ahead on flop and turn until he c/c again. Now I am not too sure where I stand, the absolute least I think villain could have is KK so I don't think I can bet the river for value. I am either only slightly ahead, splitting, or way behind.

Thoughts?