KK vs raice of a nit

Hand converted with online PokerStrategy.com hand converter:

Reproducir mano

$0.1/$0.25 No-Limit Hold'em (9 handed)

Known players:
[tg]UTG1$9.43:///////;UTG2$14.89:///////;MP1$17.46:///////;MP2$25.75:///////;MP3$27.75:///////;CO (Hero)$10.00:///////;BU$11.79:///////;SB$25.02:///////;BB$18.67:///////;[/tg]

Preflop: Hero is CO with K:h, K:c.
5 folds, Hero raises to $0.62, BU calls $0.62, 2 folds, BB folds.

Flop: ($1.59) 9:c, 4:c, J:c (2 players)
Hero bets $0.90, BU raises to $4.22, Hero raises to $9.38, BU calls $5.16.

Turn: ($20.35) 6:h (2 players)

River: ($20.35) 7:d (2 players)

Final Pot: $20.35.

Results follow:

Hero shows a pair of kings(Kh Kc).
BU shows a pair of jacks(Th Jd).

Hero wins with a pair of kings(Kh Kc).

Oponent
3k hands

14/13
c/c 2%
WWSF 46
W$SD 57
WTSD 23
AF 5
Fcbet 62
c/r 5%

I see an easy fold in flop. I dont know wht i pay.
What is your opinion?