Simple first check is to drive behind it and watch the rear tires. Try that and see if anything pops out you.
If you dont get it in the wheel, it should be in the back. Bad rim (which a static balance can overlook to an extent), bent axle shaft, bad wheel bearing, broken belt (balance guy should catch that).
Any ways, follow the wife for a quick jaunt down deefoot. Free, fast, and might tell you something.
Did either rear tire take a seemingly excessive amount of weight to balance? That would be a good clue.