I mean, I kept looking for a spot to push, or reraise or whatever, but this douche just kept calling, so I couldn't make any of my signature plays. So, what do I do on the river?

Villain 30/4/1.13

Party Poker No-Limit Hold'em, $ BB (10 handed) from (Format: Bet The Pot)

Hero ($27.45)
BB ($4.75)
UTG ($35.30)
UTG+1 ($39.65)
UTG+2 ($29.22)
MP1 ($0)
MP2 ($7.90)
MP3 ($7.44)
CO ($28.80)
Button ($5.65)

Preflop: Hero is SB with , . Hero posts a blind of $0.10.
2 folds, UTG+2 calls $0.25, 4 folds, Hero (poster) completes, BB checks.

Flop: ($0.75) , , (4 players)
Hero bets $0.5, BB folds, UTG+2 calls $0.50.

Turn: ($1.75) (3 players)
Hero bets $1, UTG+2 calls $1.

River: ($3.75) (3 players)

Well if he just keeps calling you down, then I wouldn't bet anything on the river. I'd check/fold the turn and check/fold the river. Wait until you have an actual hand.