Is it a feel, hear, or both type of vibration?
Weight on the seat could close the gap on something in the seat. The entire truck will shift to the passenger side changing angles in the suspension, but not sure why it would change a vibration. Maybe something in the exhaust is just barely contacting. Are the heat shields tight?
It isn't a rattle caused by something being loose. It is a vibration. I did find that my drive shaft was not in phase so I rectified that as well as shifted my gear around so that more weight is on the passenger side. Will report back tomorrow on the results.