Live 3/6-SB Complete BB raises ?

[Alfil]

SB is $2 so in general I've been completing with nearly any two with 4+ limpers but when the BB raises and its called around I've been tossing my hand. I'm under the impression that I might be playing too tightly and am wondering what range of hands are callable when the pot is 10+ bets preflop. In conjunction when one has a read on what the BB is raising with- PP 10+ and Broadway J 10+ what range is worth seeing a flop for one more bet?