Anybody know the biggest tire a stock YJ spare tire carrier will handle?

It will sort of handle the stock tire.....

Seriously I've seen several of those carriers crack with just 31s on them. Carrying anything like a 33 or larger, is just asking for tailgate or tub damage. The hinges just won't handle the weight. A tire carrier is the real solution.

It will handle up to a 30" but bigger than that and your going to have problems. Not much you can do to make it work any better except a swing away bumper mounted carrier.