NL10 SH, awkward position with set

$0.05/$0.10 No Limit Holdem
PokerStars
3 Players
Hand Conversion Powered by weaktight.com

Stacks:
HERO (BTN) ($12.20) 122bb
SB ($3.36) 34bb
BB ($15.33) 153bb 17/12, AF: 3.3, 3B: 5, 60h

Pre-Flop: ($0.15, 3 players) HERO is BTN 3♠ 3♥
HERO raises to $0.25, SB folds, BB calls $0.15

Flop: K♠ 3♦ J♦ ($0.55, 2 players)
BB checks, HERO bets $0.35, BB raises to $1.20, HERO calls $0.85

Turn: Q♥ ($2.95, 2 players)
BB bets $2, HERO raises to $4, BB calls $2

River: 6♦ ($10.95, 2 players)
BB goes all-in $9.88, HERO?

PRE
Standard.

FLOP
He`s basically X/R`ing with KJ or FD`s. Standard obviously would be to go over the top, which I probably should have done, because he`s not bluffing often enough to slow-play.

TURN
I had to raise more, like 5$. Shoving is not too bad either.

RIVER
2-pair is not playing this way, he would have gone broke on the turn. I guess this is a fold.