You say that you don't re-raise because you are afraid to jeopardize your stack on the bubble, but I actually think re-raising is the safer way to play it. There are only two hands you are afraid of before the flop, and obviously a big stack raising from middle position is going to have a much wider range than those.

Once you don't re-raise, you are giving the many worse hands he could be playing a chance to outflop you.

Unless there is an A or K on the flop, it's going to be virtually impossible for you to get away from the hand, so if you call here, it should be for the purpose of trapping Villain when he flops a pair worse than QQ. In other words, calling is a higher variance line that may marginally +EV versus re-raising (though I'm not convinced it is). But if you're concerned about stack preservation, you have to re-raise. You can even push, if you're really worried about it- Villain may interpret this as a re-steal with a weak hand.

I'm not generally an advocate of wimpy bubble play, but I think re-raising QQ is definitely less likely to get you busted than playing it out of position on the flop, and I think calling is at best very slightly +EV if you think Villain will fold to a re-raise but go all the way with a weak one pair hand or make a continuation bet that you can snap off. You are far more likely to trap yourself, in my opinion.