Actually, the F-150 sway control is an interesting beast. I tow a Bullet Premiere 31BHPR and I can feel cars passing me at times. When large trucks come barreling by we can get a nice push but the F-150 sway control never says a word.
Coming home from Myrtle Beach a year ago we were in the Blue Ridge Mountains in a high wind warning and coming down hill we'd hit bridges over the bottom of the valley and the curtain of trees would end so the wind had a free shot. Most of the time I wouldn't feel a thing but the sway control would kick in, the cruise would be knocked off and the brakes applied for a second. My usual reaction was to hit resume on the cruise and carry on.
I have only had the F-150 complain a couple of other times in the 4 years of towing this rig over 12,000 miles.
I'd make sure your hitch is set up properly and that the tongue weight etc. is correct. If all that is in order then I'd get a new sway system for the trailer.