Joe,
You and I are talking about apples and oranges. The driver needs to get the tongue weight of the trailer (your method will work without an equalizer hitch) in order to determine that the CG of the trailer is far enough ahead of the axles to provide stability.
As long as the CG is satisfactory, with about 15% of the trailer's weight on the hitch, then an equalizing hitch will spread that hitch weight around. Compared to being hitched up without the equalizing feature, an equalizing hitch will increase the weight carried by the truck's front axle and the trailer axles, and decrease the weight carried by the truck's rear axle. With an equalizing hitch, the truck doesn't wind up carrying the full hitch weight because some of that weight is transferred back to the trailer axles.
In other words, the tongue weight of the trailer is not the effective weight that the trailer puts on the truck, as long as an equalizing hitch is used. Without an equalizing hitch, you are correct, the hitch weight is entirely carried by the truck.
Without an equalizing hitch, the rear axle of the truck will carry more than the hitch weight, and the front axle load will decrease by a little bit. Note VC's last post.
Bombero,
Adjusting the equalizing hitch to provide greater weight on the truck's trailer hitch ball will not move the CG of the trailer forward. It will merely redistribute the weight that is already there.
Your problem is not that the truck is not carrying enough weight, but rather that your trailer CG is too far back (close to the axles) to provide sufficient stability. You won't solve your problem by adjusting the equalizing hitch. You need to adjust the load on the trailer to move the CG forward to get the stability you need to avoid sway.
VC,
If your weights using both methods were within 10 pounds of each other, congratulations. That's better than I've been able to do. I consider Joe's method of determining hitch weight the easiest. Weigh the truck empty, then weigh just the truck axles with the trailer hitched up (no equalizing hitch allowed). The difference is the hitch weight. Weighing the force on the jack is pretty close to hitch weight, as long as the jack isn't too far back, as it is on gooseneck and fifth-wheel trailers.
You certainly can use the numbers you got as the hitch weight.
Happy towing,
Loren