If this is something new then I would start checking a couple things:
1) Did something break/bend that has caused the rear end to move?
2) Have I bent an axle tube
3) Do I have a suspension component that is failing like shock, airbag, etc.
It doesn't hurt to measure the rollout on both tires.
If everything is up to par, I would get it on scales and find out what is going on weight wise.