NL10 - JJ 3 Aces on Board....Check River?

[jlp_2908]

Party Poker, $0.05/$0.10 NL Hold'em Cash Game, 9 Players
LeggoPoker.com - Hand History Converter

MP1: $9.90
Hero (MP2): $23.47
CO: $2.09
BTN: $16.39
SB: $9.90
BB: $1.35
UTG: $7.91
UTG+1: $18.72
UTG+2: $1.30

Pre-Flop: J[img]/images/graemlins/heart.gif[/img] J[img]/images/graemlins/spade.gif[/img] dealt to Hero (MP2)
UTG calls $0.10, 3 folds, <font color="red">Hero raises to $0.55</font>, 4 folds, UTG calls $0.45

Flop: ($1.25) 9[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] (2 Players)
UTG checks, <font color="red">Hero bets $1</font>, UTG calls $1

Turn: ($3.25) A[img]/images/graemlins/spade.gif[/img] (2 Players)
UTG checks, <font color="red">Hero bets $3</font>, UTG calls $3

River: ($9.25) 4[img]/images/graemlins/club.gif[/img] (2 Players)
UTG checks, Hero checks

Ok I realize villian only has a little bit left, but regardless of stack size( say he had like 50bb more) would a check be the best move? Or I probably should bet it since he might call with just about any pp.... Vil was fairly tight

How were my bet sizes etc?