Avoid action aganist weaker player?

Full Tilt No-Limit Hold'em, $0.50 BB (2 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

BB ($45.75)
Hero (SB) ($110.70)

Preflop: Hero is SB with K, 5
Hero bets $1.25, BB calls $0.75

Flop: ($2.50) 5, 5, 9 (2 players)
BB checks, Hero checks

Turn: ($2.50) 3 (2 players)
BB bets $2, Hero calls $2

River: ($6.50) 6 (2 players)
BB checks, Hero bets $3, BB raises to $42.50 (All-In)

Total pot: $12.50

Results below:
Hero didn't show K, 5 (nothing).
BB didn't show
Outcome: $3.12 returned to BB$3.12 returned to Hero

What do you think?
if you need history with this player I will give.