[Closed] TP vs. shortstack's shove

Villain is sth. like 60/15/3.5 on few (30) hands.
Preflop, flop, and probably also turn seem standard to me. I decided to rather check flop and villain (shortstack) shoves. How do you suggest me to react? Top pair with good kicker might generally be OK vs. shortstack, yet I'm not sure it holds in this spot.

Hand converted with online PokerStrategy.com hand converter:

Play hand

$0.05/$0.1 No-Limit Hold'em (4 handed)

Known players:
[tg]BB$4.90:///////;CO$21.99:///////;BU$11.84:///////;SB (Hero)$11.14:///////;[/tg]

Preflop: Hero is SB with K:d, J:c.
2 folds, Hero raises to $0.40, BB calls $0.30.

Flop: ($0.8) 9:s, 3:c, K:c (2 players)
Hero bets $0.57, BB calls $0.57.

Turn: ($1.94) 7:c (2 players)
Hero bets $1.10, BB calls $1.10.

River: ($4.14) 8:d (2 players)
Hero checks, BB raises to $2.83, Hero ???

Final Pot: $4.14.