Value Towned Myself

Should I be checking behind this river? No real reads on villain.

PokerStars No-Limit Hold'em, $0.10 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

saw flop

Button ($10.45)
SB ($10.45)
BB ($11.30)
UTG ($10)
UTG+1 ($12.10)
MP1 ($5.65)
MP2 ($5.65)
Hero (CO) ($10)

Preflop: Hero is CO with 9, J
3 folds, MP2 calls $0.10, Hero raises to $0.50, 3 folds, MP2 calls $0.40

Flop: ($1.15) 9, 4, K (2 players)
MP2 bets $0.20, Hero calls $0.20

Turn: ($1.55) J (2 players)
MP2 checks, Hero bets $1.20, MP2 calls $1.20

River: ($3.95) 3 (2 players)
MP2 checks, Hero bets $3.75, MP2 calls $3.75 (All-In)

Total pot: $11.45 | Rake: $0.55

this is good

I'm never checking behind because I have two pair, and he's a shortstack. He's calling you with a king.