25NL - KK vs weird line

[VLV]

Villain is 38/28/0.8 over only 39 hands.

Full Tilt Poker - No Limit Hold'em Cash Game - $0.10/$0.25 Blinds - 5 Players - (LegoPoker (http://www.legopoker.com) Hand History Converter (http://www.legopoker.com/hh))

SB: $25.10
BB: $60.10
UTG: $32.50
Hero (CO): $26.15
BTN: $7.90

Preflop: Hero is dealt K/images/graemlins/heart.gif K/images/graemlins/diamond.gif (5 Players)
UTG folds, <font color="red">Hero raises to $0.85</font>, 2 folds, BB calls $0.60

Flop: ($1.80) T/images/graemlins/heart.gif 7/images/graemlins/heart.gif 5/images/graemlins/diamond.gif (2 Players)
<font color="red">BB bets $1.80</font>, <font color="red">Hero raises to $5.50</font>, BB calls $3.70

Turn: ($12.80) 4/images/graemlins/club.gif (2 Players)
BB checks, <font color="red">Hero bets $10.00</font>, BB calls $10.00

River: ($32.80) 8/images/graemlins/diamond.gif (2 Players)
<font color="red">BB bets $32.80</font>, Hero ???

I only have $9.80 left, so I'm getting odds of just over 3:1, I feel like I'm behind but can I fold this?

[TheRenaissance]

I snap call. Getting such good odds, the times he has a missed draw will more than make up for it.

[CrustyFace]

Looks like he might be trying to bluff the river on a missed draw, since he checked the turn.