You need to go weigh your rig. Take a trip to the local Cat scale
and get 3 basic weights with truck and trailer loaded, ready to camp, all people and pets that will be in it when towing and a full tank of gas. You will put front axle on scale pad one, rear axle on scale pad two and both tt axles on scale pad 3. First weight will be tv no tt. 2nd weight will be tv plus tt no wdh. 3rd weight will be tv and tt with wdh. The difference in tv axle weights between first and second weigh in will be your actual tongue weight. The difference between total weight in weighs one and two will be your actual trailer weight. I'm willing to bet you have way more than 200 lbs of gear added. Just propane and batteries will add clause to 100 lbs to unloaded weight. Clothes, dishes, chairs, firewood, tools, revelers, toiletries, etc all add up a lot quicker than you think. On average people add 1000-1500 lbs of stuff to their trailer (some a little more, some a little less).
The third weight will help you figure out if your wdh us set up correctly. Ideally you want to bring the front axle as close to unloaded weight as possible without going heavier. this
Will help you understand how to set your hitch better.
Now let's return to the first scale weight. Take the total weight of tv and subtract it from the tv gcwr to get your adjusted towing capacity. Your tt needs to weigh less than this loaded. Take the total tv weight and subtract it from the tv gvwr to get your available payload. Your tongue weight must be less than this. Also check your max rawr and make sure your loaded rear axle weight with wdh adjusted is less than this.
Now let's talk about other causes of sway and handling issues. Too light tongue weight is a big cause. Ideal tongue weight is 13-15% of loaded tongue weight. If the tt is too heavy in the reAr, then it will cause sway. Too heavy tongue weight can also cause handling issues. Remember true sway is side to side oscillations with increasing speed and distance in the oscillations. Trailers will get a slight wander when towing. You can also get bow wave effect from a semi passing you (it will push you out and then suck you in). This will exist but shouldn't be unreasonable. If your front end feels like it is skating.g on the road, you are probably too light up front causing an understeer condition. Too heavy on the truck front axle will result in an oversteer condition or too much bite in the road from your tires. Porpoising motion will be a wdh adjustment. If you are getting tail wagging the dog or trailer controlling the truck, you might have too much tt for the truck. P rated tires have a lot of flex in the sidewall for comfort. This does not help with towing g, you will 've more "squirrelly" on the road. Upgrade to LT tires, if your rims can handle them look at load range E tires. A lot of info but hopefully something in here will cover your true problem.