Turtle... I have not measured the tongue weight. Not even sure there is anywhere near me with the capability of doing that.
TXIce... Sunset trails ships there trailers with a certified dry weight equipment included. Each unit is weighted on delivery and individually marked. I am going on memory because the rig is not at home but mine came in at 6982lbs.
When I bought the rig I assumed 1500lbs in cargo/people/stuff and wanted plenty of room to spare which was why I went shopping with a 7000lb limit. I have towed this set up this year with 6 grown men and a weekend of beer in the truck, easily outweighing my family trips by 1000lbs and had no issues at all.
I know my towing weights are the obvious easy answer to this issue. And if the sway problem was consistent I would suspect that was the correct answer. But reality is out of 9000km of travel the sway problems have only occured on two days and both times after three straight days of towing.
Truck length is an issue, the short box wheel base is going to struggle with a longer trailer, but again that does not account for the inconsistent performance. Tire pressure was checked prior to the trip on both vehicles and was in very good shape, as noted my only concern there was when we hit record temps inthe South that expansion may have over inflated the tires.