I voted fold before checking, but it looks like it's really close and a matter of ranges once I plugged it into SNGPT. Assuming BB knows you, he probably ought to be calling a reasonably wide range, at least top 20-25%. That alone won't make it a fold, but BB ought to be calling a fairly similar range, and even if he's as tight as 15% it's only about break-even.

I guess it all depends on how likely you think it is big stack will finally realize how many chips he has. I'm guessing he's eventually going to decide he's had enough of you stealing the blinds he wants to take...