JJ in BB Gets Limp/Re-raised By A Monkey

Poker Stars, $0.50/$1 NL Hold’em Cash Game, 9 Players
LeggoPoker.com – Hand History Converter

SB: $59
Hero (BB): $105.95
UTG: $17
UTG+1: $35.35
UTG+2: $19.40
MP1: $25.35
MP2: $202.35
CO: $63.90
BTN: $91.50

Pre-Flop: J J dealt to Hero (BB)
5 folds, CO calls $1, BTN folds, SB calls $0.50, Hero raises to $6, CO raises to $11, SB folds, Hero???

Villain is 49/5/4.3 over 55 hands, I have conflicting thoughts in these situations, the guy is obviously horrible, but at the same time his limp/re-raise is kind of scary given how little he raises pre-flop. Shoving doesn’t feel right and playing for set value feels weak, what to do?