stabalizer or equalizer bars? equalizer bars don't do anything for sway, maybe make it a little less just because of the added tension, but they are generaly the solution for porposing.
generaly, sway comes from improper loading of the trailer, hitch to light. when you say you checked the hitch weight, what percentage of it is of the total rv weight, and was the trailer loaded for camping? you want it to be a minimum of 10% and preferably up to 15%. so that means if your rv is 8000lbs ( loaded full of water) you want that hitch weight to be a minimum of 800lbs and up to 1200lbs idealy. if you measured when you were empty the hitch weight most likely changed when you got it loaded up. there are other things that can cause it also, suspension worn out, very strong winds, tires underinflated, hitch not adjusted properly, excessive speed and vehicle wheelbase to short to control the rv. the hitch weight and tire inflation are the easiest ones to start with.