Pug fugly set hand... your move?

Party Poker No-Limit Hold'em, $ BB (10 handed) FTR converter on zerodivide.cx

UTG+1 ($39.65)
UTG+2 ($122.55)
MP1 ($58.60)
Hero ($77.80)
MP3 ($63.32)
CO ($31.75)
Button ($55.60)
SB ($52.83)
BB ($44.25)
UTG ($49.50)

Preflop: Hero is MP2 with 4, 4. SB posts a blind of $0.25.
4 folds, Hero calls $0.50, 2 folds, Button calls $0.50, 1 fold, BB checks.

Flop: ($1.75) Q, 4, K (3 players)
BB checks, Hero bets $1, Button calls $1, BB folds.

Turn: ($3.75) 8 (2 players)
Hero bets $1.5, Button raises to $3, Hero raises to $6, Button calls $3.

River: ($15.75) A (2 players)
Hero bets $8, Button raises to $48.10 (all-in), Hero ???

Button was loose preflop.

I think the river was a fold, but I'm second guessing myself now. I think I should have re-raised him more on the turn, to keep the draw odds down.

Fold, the only thing you beat is a bluff.

I've seen overzealous two pairs do this, but I agree... I think it's a fold as well.