^ It's more accurate to add up the hitched front and rear axle weights. 3924 + 3110 = 7034 lbs on the axles This is the truck weight when hitched to the trailer.
You have 971 lbs hitch weight. Subtract the truck only weight from the hitched weight. 7034 - 6063 = 971 lbs tongue weight.
You lost 285 lbs from the front axle (3395 - 3110 = 285)
You gained 1,256 lbs on the rear axle. (3924-2668 = 1256)
Your tongue weight it 14.5 percent which you can find by using the tongue weight and the total loaded trailer weight. (971 / 6700 * 100 = 14.5% tongue weight)
With almost 300 lbs missing off the front axle I'm betting you're getting light steering more than actual sway of the trailer.
Unfortunately it looks like you're going to need a more stout weight distribution hitch like an Equal-i-zer
Linkor a Reese Dual Cam
LinkThe leveling kit on the truck might be aesthetically leveling the truck. But it's doing nothing to transfer or re-distribute the weight which is what you really need.