The tongue weight mantra is always brought up, but almost never mentioned is inadequate rear suspension except for Myreracer . His suggestion for new rear shocks and tires are golden. Though I dislike them, adjustable Rancho shocks can be adjusted hard and will cover many suspension sins.
I towed a 10 and 1/2' StarCraft tent trailer with a '91 Jeep Cherokee. In spite of an upgraded rear suspension, we had some sway. A big cooler across the rear was bit of a dumb design. My beloved Jeep died and I upgraded to Dodge 1ton. Driving down a gravel road in the Cariboo , I looked in the mirror, "My,gawd, that trailer wags like a friendly dog's tail." I hadn't noticed until I looked !We have a travel trailer, now.
Myredracer missed this, but a simple upgrade to the truck is to add a leaf to the rear, around here, it's pretty inexpensive.
A trailer will sway with wind and road conditions. Heh, you have to steer the truck, don't you? So how come you expect the trailer to track like an arrow ? The thing is you don't want the trailer's misbehaving to affect the TV. It's not healthy for your hands to have all the blood squeezed out for those long drives.