If engine/trans mounts are worn, this will cause engine/trans to not sit right. Or, if the rear suspension was changed(ride height) this will cause issues also.

Inspect the driveshaft for any paint missing. If a welded on weight has come off, it should leave an exposed part of the driveshaft.

I purchased the truck new and at only 66,xxx mile I don't think the trans or motor mounts are the problem. I will look into the rear suspension. I am sure the truck has (compressed) suspension wise some. That would also explain why the vibration is worse while pulling a trailer. It lowers the back of the truck 1-2 ". Also the driveshaft has been checked over and the original balance weights are in place and doesn't seem to be any missing weights. How would a person get the trucks rear suspension back up to the original ride height?

Replace the rear springs, bushings etc.

The only time rear suspensions are sagged to the point of no return is if the load exceeded the carrying capacity of the truck, or a trailer sat on it for extended periods of time. With this truck being only 5 years old, I doubt age did anything.

I'd suggest OP takes the truck to a reputable tire shop with a road force wheel balancer. Have them check for wheels out of round, tires out of round, and tires that have hard spots in them.

Has been road force balanced twice. He even replaced one tire and it did not change anything.

Does the road force balancer show zero out of round/hard spot/centrifugal out of balance on each tire? . . . or do they let it slide at some low number and say "you'll never feel that little bit"?