$5 NLHE 6-max: Check-raising turn with top pair + OESD

5NL 6-max zoom on pokerstars. Villain is unknown.

Hero (SB) has $8.54
Villain (BB) has $9.21

Hero is dealt 8c 7c
Hero (SB) posts $0.02
Villain (BB) posts $0.05
UTG folds
MP calls $0.05
CO calls $0.05
BTN folds
Hero (SB) calls $0.03
Villain (BB) raises to $0.15
MP calls $0.10
CO calls $0.10
Hero (SB) calls $0.10

$0.56 in pot (4 players)
Flop shows 8d 5s 2h

Hero (SB) checks
Villain (BB) bets $0.30
MP folds
CO calls $0.30
Hero (SB) calls $0.30

$1.40 in pot (3 players)
Turn shows 6d

Hero (SB) checks
Villain (BB) bets $0.55
CO folds
Hero raises to $2.10
Villain calls $1.55

$5.50 in pot (2 players) with effective stacks of $5.99 behind
River shows Kh

Hero checks

What do you think of the way I played this hand? Was it a good idea to check-raise the turn? Should I have followed through with the aggression by shoving on the river?

Don't bluff multi-way. BB is showing a lot of strength double barreling into three other players. He probably has an overpair here, and I don't expect a lot of people, especially at 5NL, to fold overpairs to turn raises. You don't have much fold equity here, so I'd just call down and check-fold river unimproved. As played, checking or shoving river to get him off QQ/JJ/1010/99, and possibly AA is okay.