I am not sure whether I should 4bet here and whether I should be prepared to play for stacks against this villain.

$0.10/$0.25 No Limit Holdem
6 Players
Stacks:
Hero ($48.67)
UTG+1 ($25.57)
CO ($42.73)
BTN ($30.32)
SB ($27.50)
BB ($33.87)
Pre-Flop: ($0.35, 6 players) Hero is UTG J♠ J♣
Hero raises to $1, 4 folds, BB raises to $4, $3 to Hero ($47.67)?