In 2015 Ford went to the all aluminum body, and changed the shocks. Whatever they did to them made for the worst riding suspension in the F150's. Going over railroad tracks, or hitting expansion joints on a curve would cause the rear end to kick out. Hard bumps or rough roads would have the truck jiggling all over the place and I could feel double or triple rebounds as the tires bounced over bumps. Replacing the factory shocks with Bilstiens, or FOX cures that issue, but there are plenty of complaints with weird towing issues such as mine that have yet found a solution to. Others have had no complaints, but are using high end hitches such as Blue Ox or Equa-Li-Zer. There are plenty of threads on the F150 forum in regards to this issue as well.
I do know that when I had gone to the 2016, the hitch ball was too high since it sits higher than the 2014, so I dropped it to the correct height, and left everything else as is thinking the spring tension is going to be correct since the trailer hasn't changed, only the truck. Turns out it had too much spring pressure for this truck and transferred too much weight fore and aft and caused speed induced sway, above 63 MPH the trailer would sway. I removed a shim which set the head more vertical, and reduced spring tension. Now the truck and trailer move as one, and it no longer has speed induced sway. I am very confident that my axle weights are proper, but will get the rig weighed at some point, reason I haven't, this truck has a higher payload, and since I know the TW and trailer weights from the 2014 and were within it's payload, I haven't felt a need to weigh it.
There are a few design changes to the suspension as well, they moved the drivers side rear shock to the rear of the axle, the springs are different, my last truck has 3 leaves, this one 2, and the frame is different, the metal thickness is less in some areas. The axles are the same, yet have a lower GAWR. I also know this truck sinks down lower when the trailer is dropped on it, but once the WDH is snugged, then the well height difference is about the same as the 14.
This isn't a weight distribution issue, its a suspension issue as I can see the truck moving in ways it shouldn't when on uneven roads. This movement translates back to the trailer causing it to move. So it boils down to, what on the truck needs to be corrected. I really don't want to buy a new hitch since I know the one I have worked properly on the 2014, so if adding something like Sumosprings to reduce body roll, which is what I believe the issue is, can solve it, then that would be the way to go.