Tongue weight, and tires are all important. Also VERY important is getting the hitch adjusted correctly. Are you returning the front end of the TV to the road. Meaning, IF you have it wrong. Your front / steering axles are light, and this cause sway. it causes the steering to be VERY easy, and makes it easy to over steer. If you plant the front axle back onto the road. That will return steering control to the steering wheel.
so check your front measurements un hooked, and hooked up. The front bumper should return at LEAST 1/2 of the distance it raised with out the WDH installed. I prefer it to come back all the way to the unhooked measurement. but that is just me.
read your WDH instructions to find your best measurements. A incorrectly adjusted hitch will get you in trouble. The trailer should not sway in normal driving WITHOUT a sway bar installed. IF it does you have other problems. Fix it, and then add sway control.