Hand converted with online PokerStrategy.com hand converter:
$0.02/$0.04 No-Limit Hold'em (2 handed)
Known players:
[tg]SB$12.70:///////;BB (Hero)$5.01:///////;[/tg]
Preflop: Hero is BB with K:d, 9:d.
Hero raises to $0.12, SB calls $0.08.
Flop: ($0.24) 6:d, A:d, T:d (2 players)
SB checks, Hero bets $0.17, SB calls $0.17.
Turn: ($0.58) 3:d (2 players)
SB checks, Hero bets $0.42, SB calls $0.42.
River: ($1.42) 3:h (2 players)
SB checks, Hero bets $1.24, SB raises to $3.80, Hero raises to $4.30, SB calls $0.50.
Final Pot: $10.02.
And otherwise Bet a bit smaller on the river he will have hard time to Call with a lot worse. And as you get raised what do you expect to beat there? I would say even easy fold while the board paired, you are most likely against FH.