You need to weigh your set up before you go spend money on a heavier duty truck.Reality, the problem may be the trailer with too little hitch weight. Too much weight from side to side. Trailer axles that are V'd vs perpindular to the middle of trailer.
You might even have a trailer where the axles are too far forward to have enough hitch weight. Even with a 25/35 series truck, your trailer will still want to fishtail sway.
Look at what is the cause of the effect before spending money.
I've towed over ratings for many decades, most of the time I go slower than I like, due to too little motor. BUT, if everything is set up correctly, I have no towing effects like sway!
Marty