KK on A-high flop

[Saborion]

Party Poker No-Limit Hold'em, $1 BB (9 handed) converter

Nothing on my opponent.

SB ($39)
BB ($50)
UTG ($151.40)
UTG+1 ($84.48)
MP1 ($51.10)
MP2 ($126.30)
MP3 ($47.80)
CO ($64.15)
Hero ($99.50)

Preflop: Hero is Button with K[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/spade.gif[/img].
UTG folds, UTG+1 folds, MP1 folds, MP2 folds, MP3 calls $1, CO folds, <font color="CC3333">Hero raises to $4</font>, SB folds, BB calls $3, MP3 folds.

Flop: ($9.50) A[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/heart.gif[/img], 3[img]/images/graemlins/spade.gif[/img] <font color="blue">(2 players) </font>
<font color="CC3333">BB bets $1</font>, <font color="CC3333">Hero raises to $9</font>, BB calls $8.

Turn: ($27.50) 6[img]/images/graemlins/diamond.gif[/img] <font color="blue">(2 players) </font>
BB checks, Hero checks.

River: ($27.50) 6[img]/images/graemlins/spade.gif[/img] <font color="blue">(2 players) </font>
BB checks, Hero checks.

Final Pot: $27.50
<font color="#990066">Main Pot: $27.50, between BB and Hero.</font>

Now, after he checks both the turn and the river, I have a value bet? Almost similar situation as in a hand I posted not long ago, where I was told to bet the river. The difference is that in the previous hand I re-raised a PFR with QQ and the flop came A-high. In this hand, he bet into me. Either a PP, or Ax. Or?