NL25: 3rd barrel?

[stabbyah]

No reads on the guy. Just that he instachecked flop and turn and I was absolutely sure that he was on a weak ace but didnt know if he was a donk or not to fire the 3rd barrel.
Do you guys think i should have bet the river?

Poker Room skin
No Limit Holdem Ring game
Blinds: $0.15/$0.25
4 players
Converter

Stack sizes:
UTG: $6.35
Hero: $24.90
SB: $10.75
BB: $23.65

Pre-flop: (4 players) Hero is Button with 8[img]/images/graemlins/club.gif[/img] 7[img]/images/graemlins/heart.gif[/img]
UTG calls, <font color="#cc0000">Hero raises to $1.2</font>, SB folds, BB calls, UTG folds.

Flop: K[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/club.gif[/img] ($2.8, 2 players)
BB checks, <font color="#cc0000">Hero bets $2</font>, BB calls.

Turn: 3[img]/images/graemlins/heart.gif[/img] ($6.8, 2 players)
BB checks, <font color="#cc0000">Hero bets $4.5</font>, BB calls.

River: T[img]/images/graemlins/heart.gif[/img] ($15.8, 2 players)
BB checks, Hero checks, Hero folds.

Results in white:
Final pot: $15.8
<font color="#ffffff">BB bet 7.70 collected 15.05 net 7.35 shows 8d As </font>