NL2 FR AK failed cbet

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.01/$0.02 No-Limit Hold'em (9 handed)

Known players:
[tg]MP3$2.20:///////;CO$1.05:///////;BU (Hero)$4.71:///////;SB$2.10:///////;BB$7.37:///////;UTG1$3.63:///////;UTG2$1.47:///////;MP1$2.18:///////;MP2$1.98:///////;[/tg]

Preflop: Hero is BU with A:c, K:d.
UTG1 folds, UTG2 calls $0.02, MP1 folds, MP2 calls $0.02, 2 folds, Hero raises to $0.12, SB folds, BB calls $0.10, UTG2 calls $0.10, MP2 folds.

Flop: ($0.39) 6:s, 6:h, T:c (3 players)
BB checks, UTG2 checks, Hero bets $0.28, BB calls $0.28, UTG2 folds.

Turn: ($0.95) 8:h (2 players)
BB checks, Hero checks.

River: ($0.95) Q:c (2 players)
BB checks, Hero checks.

Final Pot: $0.95.
Results follow:

BB shows two pairs, tens and sixes(9:h T:h).
Hero shows a pair of sixes(A:c K:d).

BB wins with two pairs, tens and sixes(9:h T:h).

Player was stable TAG. Best was to give up after failed cbet. So I did and think line is ok.