Ultimate Bet No-Limit Hold'em, $.25 BB (9 handed) converter

CO ($25.30)
Button ($11.20)
SB ($4.15)
Hero ($29.85)
UTG ($30.30)
UTG+1 ($24.65)
MP1 ($43.95)
MP2 ($26.65)
MP3 ($12.10)

Preflop: Hero is BB with 8, 3.
UTG calls $0.25, 1 fold, MP1 calls $0.25, MP2 calls $0.25, 2 folds, Button calls $0.25, 1 fold, Hero checks.

Flop: ($1.35) 8, A, 3 (5 players)
Hero bets $1.35, UTG folds, MP1 folds, MP2 calls $1.35, Button calls $1.35.

Turn: ($5.40) 2 (3 players)
Hero bets $5.4, MP2 folds, Button calls $5.40.

River: ($16.20) 2 (2 players)
Hero checks, Button checks.

Final Pot: $16.20

Hero has 8c 3s (two pair, eights and threes).
Button has Ac 9s (two pair, aces and twos).
Outcome: Button wins $16.20.


My question is: was it correct to check on the river? I assumed I was beat when the board paired, but I had a (small) chance of getting him to fold if I bet. Secondly, what if he had bet after I checked, should I have called? He only had about $4 left.

Flop and turn OK?