I just can't see where I am ahead here. Should or could I have played this any differently? Should I have folded the turn?

Edit for read: Villian was 20/4.8/.4 over 80 hands

PokerStars No-Limit Hold'em, $0.25 BB (9 handed) Poker-Stars Converter Tool from FlopTurnRiver.com (Format: FlopTurnRiver)

MP1 ($21.55)
MP2 ($31)
MP3 ($51.60)
CO ($9.10)
Button ($25)
SB ($45.90)
BB ($22.70)
UTG ($14.90)
Hero ($25.40)

Preflop: Hero is UTG+1 with A, Q.
1 fold, Hero raises to $1, 6 folds, BB calls $0.75.

Flop: ($2.10) A, 5, 8 (2 players)
BB checks, Hero bets $1.5, BB calls $1.50.

Turn: ($5.10) 4 (2 players)
BB bets $4.25, Hero calls $4.25.

River: ($13.60) A (2 players)
BB bets $15.95 (All-In), Hero folds.

Final Pot: $13.60

Results in white below:
BB doesn't show.
Outcome: BB wins $29.55.