Yeah to really help we'd need more info on the trailer (tongue weight and empty weight/loaded weight).
That said, it sounds like you've got a standard weight distribution hitch with a standard separate friction sway control (my personal favorite setup, not favored by others). Messing with the chains won't help your sway issues - that's only to adjust your tongue weight and get everything level.
What you need to do is tighten your friction sway control bar more. Generally you should be able to do this with the lever, just give it a little more. That should really help your sway.
For instance, I've got my '17 PW, and I pull about a 33' camper, about 700 lbs of tongue weight, camper itself when loaded weighs only about 7000 lbs. It's an ultra-lite style camper, so aside from it being a big sail back there I really don't even notice it. But I had to learn a lesson the hard way.
See, when we picked it up I let the camper dealer set everything up, and on corners the sway control was snapping and popping like crazy. So on our first trip, I did what I always used to do on other TTs - I put the sway bar on, then bounced it up and down while I tightened the lever until it quit bouncing, then gave it about another turn.
Wooooo boy. I couldn't run 60 mph without the trailer swaying like mad. It was DANGEROUS. So...I pulled off at the next exit, and cranked that sway bar another couple turns - I mean it was getting hard to turn it, but I still had threads left so there was still more adjustment. Pulled back onto the e-way.
Night and day difference. No more sway all the way to 65 mph, and only a little bit when we got passed by a couple idiot truckers and campers (truck speed is legally 65 in my home state). So now that's how I tow - Set the cruise around 62-63, with the sway bar cranked down tight. But like I said, I'm pulling a really light, fairly long camper. Yours might be different.
