Vagtastic play with KK in weird 3bet pot

[hesheatingup]

I've seen villain on at least 2 tables of 1Knl before, thats about all I have to go on. If you play it like me are you calling a river shove? Thoughts on turn betsize? I think this might be where I went wrong, left me with only 600 on river and so a shove felt too thin. Original raiser is a ratholer.

Party Poker
No Limit Holdem Ring game
Blinds: $5/$10
6 players
Converter

Stack sizes:
UTG: $1000
UTG+1: $254.50
CO: $1077
Button: $1486
SB: $1024
Hero: $1272

Pre-flop: (6 players) Hero is BB with K[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/spade.gif[/img]
UTG folds, <font color="#cc0000">UTG+1 raises to $30</font>, CO calls, Button calls, SB folds, <font color="#cc0000">Hero raises to $165</font>, UTG+1 folds, CO calls, Button folds.

Flop: Q[img]/images/graemlins/club.gif[/img] T[img]/images/graemlins/diamond.gif[/img] 3[img]/images/graemlins/heart.gif[/img] ($395, 2 players)
Hero checks, CO checks.

Turn: 5[img]/images/graemlins/heart.gif[/img] ($395, 2 players)
<font color="#cc0000">Hero bets $300</font>, CO calls.

River: 4[img]/images/graemlins/spade.gif[/img] ($995, 2 players)
Hero checks