This is my third or fourth orbit at the table. SB is a taggish player. BB is a loose passive half stack.

What I'm wondering about is the turn bet. Given BB's stack size, I thought betting was best.

PokerStars No-Limit Hold'em, $0.10 BB (6 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

saw flop

CO ($11.10)
Hero (Button) ($10.15)
SB ($17.35)
BB ($5.35)
UTG ($11.50)
MP ($10.30)

Preflop: Hero is Button with 10, 9
3 folds, Hero bets $0.40, SB calls $0.35, BB calls $0.30

Flop: ($1.20) 8, 6, 10 (3 players)
SB checks, BB checks, Hero bets $0.80, 1 fold, BB calls $0.80

Turn: ($2.80) A (2 players)
BB checks, Hero bets $1.50, BB calls $1.50

River: ($5.80) 8 (2 players)
BB bets $2.65 (All-In), Hero folds

Total pot: $5.80 | Rake: $0.25