From the way its discribed , im thinking a bit of sidewall roll in the TV rear tires thats why i asked what kind of sway. A slight feeling of sway in the rear can be due to underinflated tires, or needing something with a stiffer sidewall. I know some are aginst LTs on a 1/2 ton. But i had this myself when i gad the half ton. Lt tires fixed it. The rear was moving a bit, enough so you had to make a lot of small corections while driving. This feeling was worsened buy any outs5ode force as the op descibed. Yes, toung weight is always importent. And knowing you weights.but sometimes its a combination of things.