You may consider a couple of things first. With your truck and trailer loaded for camping, go to a Cat scale to determine your tongue weight. The optimal ratio of trailer weight on the tongue is 13 percent. A tongue that is too light (trailer back heavy) can cause sway. The next thing I would consider is to take a look at truck tires. If you have the standard tow package, you likely have P rated tires that have softer sidewalls and can promote trailer sway. You could consider upgrading to D or E rated LT tires.
Lastly when you weigh your setup see if you are exceeding payload of the truck. 7500 is quite a bit for the truck you describe. My guess is your tongue weighs about 1000 lbs.