Poker Stars, $0.02/$0.05 No Limit Hold'em Cash, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.
Hero (SB): $5 (100 bb)
BB: $5 (100 bb)
MP: $4.61 (92.2 bb)
CO: $4.88 (97.6 bb)
BTN: $5.20 (104 bb)
Preflop: Hero is SB with J♠: J♣:
3 folds, Hero raises to $0.20, BB raises to $0.60, Hero calls $0.40
Flop: ($1.20) 6♥: 4♦: 8♣: (2 players)
Hero checks, BB bets $0.77, Hero calls $0.77
Turn: ($2.74) T♥: (2 players)
Hero checks, BB checks
River: ($2.74) 3♦: (2 players)
Hero checks, BB bets $3.63 and is all-in, Hero folds
Results:
Spoiler
$2.74 pot ($0.11 rake)
Final Board: 6♥: 4♦: 8♣: T♥: 3♦:
Hero mucked J♠: J♣: and lost (-$1.37 net)
BB mucked and won $2.63 ($1.26 net)
Spoiler

I didn't know what to do 1) My opponent still could have QQ+, but why did he check turn on the drawy board?
His w$sd = 55, but AFR = 35, so he still can be bluffy.
What should I do on the river?
Thanks.