AZJeepRubicon

I have heavy 35s (85lbs each) on my 2012 unlimited rubicon. Stock axles. Would I be adding any stress if I were to switch to 37s that were the same weight or lighter?

Invest2m4

Yes. First off, more traction offroad. Second, more moving energy due to diameter. Third, you'll likely need to push the wheels out further for clearance, which will add more leverage. That all said, what you should have done to beef your axle housing already, should be enough (truss/sleeve and gusset).

It will also wear ball joints and hubs faster. As well as steering components.