Can a higher receiver cause sway?

Thanks for the clarification on the "P" tires. That's what I suspected. Not so sure tires are in the budget right now. Just recently put the Bilsteins on and that seemed to help some. No long trips planned anytime soon. It seems as though it's going to be a combination of things. Obviously a 3/4 ton would have solved everything, but DW wanted a Suburban and I couldn't find a low mileage 3/4 ton. I'll continue to work on the individual components and reach satisfaction at some point. I have located a bolt-on hitch from an 04 that seems like it will bolt on to the frame. I may try it, just to see. The factory receiver "cross-member" is made lighter material than a regular hitch. I would not expect that to be a problem, but I'm looking for something that is different from the other 2 vehicles.