50NL KK--pot control or stack off?

[Supwithbates]

Villain is 40/0/0 over 70 hands.

Poker Stars - No Limit Hold'em Cash Game - $0.25/$0.50 Blinds - 5 Players - (LegoPoker Hand History Converter)

SB: $43.55
BB: $62.75
Hero (UTG): $57.40
CO: $55.90
BTN: $54.80

Preflop: Hero is dealt K[img]/images/graemlins/diamond.gif[/img] K[img]/images/graemlins/heart.gif[/img] (5 Players)
<font color="red">Hero raises to $2.00</font>, 3 folds, BB calls $1.50

Flop: ($4.25) 9[img]/images/graemlins/heart.gif[/img] 7[img]/images/graemlins/diamond.gif[/img] 4[img]/images/graemlins/club.gif[/img] (2 Players)
<font color="red">BB bets $4.50</font>, <font color="red">Hero raises to $10.00</font>, BB calls $5.50

Turn: ($24.25) 7[img]/images/graemlins/spade.gif[/img] (2 Players)
BB checks, <font color="red">Hero bets $15.00</font>, BB calls $15.00

River: ($54.25) 9[img]/images/graemlins/diamond.gif[/img] (2 Players)
BB checks, Hero checks

Pot Size: $54.25 ($2 Rake)

Overbet donk is atypical for him. He's fully capable of having 94o here for two pair, as well as TT-AA. Top pair seems unlikely, and I doubt he'll call off much if he has anything worse than that.

Flop minraise for information/value, I decided facing his donk I didn't want to immediately throw pot control to the wind and try to make this an all-in pot. Board played out poorly so I continued playing for pot control.

Is this losing value vs. such a station?