Technically, you're probably in spec. I would check what your actual loaded weights are at a CAT scale. Dry weight is very deceiving. Depending on the manufacturer and dealer added features, that weight could be off by 1000 lbs or more (yes, I have some experience here).
A SWB vehicle is not an ideal tow rig. You'd be better off with a Suburban or Yukon XL. I would see what brand of WD hitch you have there is. If it's one of the older chain snap-up units w/an adjustable friction bar I'd ditch it in a heartbeat. What you need is a Trunnion-style hitch like the Equal-i-zer or Fastway E2. Another good option is the Andersen hitch.
You'll need a brake controller. I really liked the Tekonsha P3. It's a digital proportional unit and is one of the best ones out there.
I have a 2010 Esky ESV and don't tow with it any longer. You've got a newer generation truck there and a slightly lower (probably) tow weight. I never had issues with sway but I also had the longer wheelbase and the Fastway E2 flat bar trunnion hitch. The truck would pull the camper just fine. What made me stop towing with it was the constant fixing of suspension, transmission, engine mounts, and the constant fear of running too hot and blowing something up. These trucks are not an ideal tow vehicle. If you're going to be towing regularly and at long distances I'd look at a 3/4 ton truck.
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