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.

Your hand has solid showdown value, even though this board is littered with draws and completions.

Checking behind river seems a sensible option, unless
a) you know for a fact that villain is capable of repping scary boards or
b) very passive with big hands and/or can make big folds
c) know exactly what to do if reraised

a better option would be to bet that flop. It looks like the prefect probe bet imo.

Bet the flop!

The river fold was good... but the rest of the hand was totally butchered.

Bet this flop, you're surely ahead and you want to build a pot. You will get a lot of calls from worse hands. Then keep betting

bet every street, fold river as played. Cash games are simply about making the best decision, don't try to fold simply because you can find a less marginal spot to take his money. The right decision is fold in this situation though.