I kinda agree with pocket fours here.

Normally I'd felt this in a second but my image is never "really tight" like OP stated.

If our image is tight, and we raised UTG and he's STILL c/r'ing us here with BB yet to act, I don't think this is a weak hand.

I don't think our push has any fold equity on the flop. I don't mind flat calling his raise since we have position. If we're tight, he'll have to respect our call wtih a mediocre hand. If he keeps firing, it might be ok to let this go.