No not normal, but it is more pronounced when a half ton truck is utilized to pull such a large rig. The thing with sway is it can go from moderate sway to out of control sway in a matter of seconds and by the time you realize what is happening it's too late.
We are neighboring states and we know a bit about how the wind blows in our neck of the woods, I wouldn't chance towing at highway speeds if even I had just a little sway. Too worried about the sudden wind gusts we get crossing through all the canyons out here.
One option is to try WD hitches from Propride or Hensley that can provide some relief by deterring sway before it gets too out of hand. We also utilize a Reese WD/SC hitch and experience no sway towing our 32' 9500# TT at interstate speeds with our Chevy 3/4 ton HD gasser.