Kings on monotome flop

[MrWooster]

This hand puzzled me a bit, only 10 hands on villain but nothing strange about him.

Prima Network No-Limit Hold'em, $0.10 BB (6 handed) Hand History converter Courtesy of PokerZion.com

saw flop|<font color="#C00000">saw showdown</font>

SB ($33.56)
BB ($6.58)
UTG ($8.44)
Hero ($9.75)
CO ($4.87)
<font color="#C00000">Button ($8.28)</font>

Preflop: Hero is MP with K[img]/images/graemlins/club.gif[/img], K[img]/images/graemlins/diamond.gif[/img].
UTG calls $0.10, <font color="#CC3333">Hero raises to $0.4</font>, <font color="#666666">1 fold</font>, Button calls $0.40, <font color="#666666">2 folds</font>, UTG calls $0.30.

Flop: ($1.35) J[img]/images/graemlins/diamond.gif[/img], 2[img]/images/graemlins/diamond.gif[/img], 4[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
UTG checks, <font color="#CC3333">Hero bets $0.67</font>, Button calls $0.67, UTG folds.

Turn: ($2.69) 3[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets $1.34</font>, <font color="#CC3333">Button raises to $2.68</font>

Villains minraise is strange and scares me a bit so I don't really want to push. Would calling the turn and folding to a river shove be a good line?