3 players, button play

I was playing a table which changed down to 3 players when I was dealt j9os on the button.

The BB is 46/4.5/ (0.7 postflop)
while
The SB is 26/16.9/ (2.2 postflop)

I was really in a difficult situation because I was unsure what the best play was. I have position over both players which is good, and J9 is an average hand. The BB who has to invest 1 dollar is pretty loose, with a WTS 50 and W$S 39 so a pretty bad all around player.

What is the best play here, do we try and push out the SB who is tight aggressive, and try and demolish the BB postflop.

Do we call because we don't want to invest much with this mediocre holding when we probably aren't going to push the BB out of the hand.

Do we fold because our hand does not hold enough value to continue from here?

True