I think I'd go broke in this spot if he had me beat. Statistically, he's far more likely to have a lone J than AA, JJ, or the case 6. I think it's even more likely given the cold call of the pre-flop raise. Would he do that with AA or any hand with a 6 in it? You're right that you're more likely to be beat as more money goes into the pot, but I still don't see how you could ever be sure enough that you're beat to justify folding.