One way to conceptualize this is when you separate the tow vehicle from the trailer, all that is left on the trailer is the snap-up brackets (or eqivalent) and the weight of them is all that remains with the trailer. The weight of the hitch shank and spring bars remains with the TV. This is why when you go to a scale, you should put the spring bars in the back of the TV when you make the pass with them disconnected. If spring bars always remained as a fixed part of the trailer tongue, it'd be different.
The measured tongue weight does not change unless you change the loading of the trailer. If it measures 1,000 lbs, it's always 1,000 lbs to the trailer. But the WDH moves this weight between the 3 sets of axles through leverage action and the TV itself sees a somewhat reduced weight - maybe 200 lbs or so less and the TV will "see" 800 lbs.
The best explanation of this on the entire internet is this:
Ron Gratz on WDH hitches It's a very good read, especially for mathematical types. Otherwise, just take his word for it. :)