CAT Scale, WDH & my math skills

My WDH manual states that when properly installed the WDH transfers weight to the TT and TV. This statement has me pondering my proposed weighing procedures.
Since I'll leave here loaded up on a Sunday my total weight will be done on a CAT scale 30 miles away. Prior to that the Tundra, which by the way will look like it's prepared for a Beverly Hillbillies movie remake, will be weighed at the local sand and gravel pit. Just as it will be before connecting the trailer. Lets just say the truck weight is 6700. Now all hitched up and the tank topped off again the CAT scale sez the total of both truck axles = 7200# and the TT weight is 4500. Does all this mean to trailer total, tongue and axles comes in at 5000# but my magical 10% number has been transferred to the hitch?
I can understand how the WDH transfers weight from the trucks rear axle to the front axle but just not wrapping my head around any transfer of tongue weight to the TT if the WDH is properly set up and the trailer remains level.
Thoughts?

 

Tongue weight is without distribution.

You need 3 measurements to start with.

Truck/trailer distributed
Truck/trailer not distributed
Truck

That middle weigh will give you your tongue weight.

For the 30 miles, assuming you adjusted your hitch with a tape measure and have good #s, I'd drive it and do the fine tuning at the CAT scale.

 

I did find this:

https://www.rv.net/forum/index.cfm/fuseaction/thread/tid/14265335.cfm

It does help me understand how the weight is distributed to the TT axle. As a pilot, weight and balance calculations are a normal part of every preflight. I see no reason to see towing a TT any different.