I notice this whenever I am on the highway. There is a bad shimmy or vibration from the rear, enough that when I look in the backseat at my son, he is shaking in his car seat. This trip I towed a jet ski trailer and the problem wasn't really there. On the way home I wasn't towing anything and it was back. The truck has General Grabber AT2s that are about a year old. Truck has ~53k miles on it, original shocks. could the shocks be the problem? The tires are rotated regularly and the problem persists so I don't think it is a bad tire or anything. I have had the balance checked three times at different places and they are fine. One shop told me that it is the tires and that I am stuck with the ride at highway speeds. Not sure that I believe that.

 

Check your driveshaft. I bent one once before, and it did the same thing. Smoothed out at 70mph, but between 45-70 it shook like a stripper. You could have thrown a weight off of it, too.