My first rig had that factory swing out carrier and it held a 32" tire just fine. Got a little bouncy off road, but it did the job. I assume you're talking about the one where the latch mechanism is in the bumper, one hinge on the body and the other hinge on the bumper corner. Just be sure that the tubes aren't rusting. They tend to rust bad at the lower hinge and at the joints.
The other carrier commonly used is the Mopar brand carrier. It mounts using several brackets to the lower right bumper corner and uses one large hinge. The latch mechanism is actually attached to the rear hatch just above the license plate. This is a solid mount for up to a 32" tire, but when you go above that, the tire/wheel weight tends to wear on the hatch mounts. Especially when you're flexing - the hatch wants to move and the carrier doesn't.
I've seen some people go to the extreme and buy a tire that is much skinnier than what they're running on the ground. Basically their version of a "space saver" spare. Say a 31x9.50 (there may be an even skinnier tire measured in milimeters, but not sure) then mounting that on an aluminum rim. You'd save quite a few pounds doing that.
Hope that helps.
