The hitch head, shank and bars go to the weight of the TV. The weight of the snap-up brackets and Reese cam arm brackets (if you have them) go to the weight on the trailer (mostly tongue wt. because of where they are). Cam arm brackets weigh about 20 lbs total and snap-up brackets about 10 lbs total. When weighing your TT and TV at a scale, put the spring bars in the TV during one of the 3 passes.
If you are planning to buy a new TT and a TV, you should not go by dry weights on the TT and on the TV, pay attention to the payload capacity. Payload capacity on the TV should also include for a full tank of fuel and everyone and everything you would take for camping which can easily be 300 - 500 lbs, plus the WDH. Then whatever payload capacity is left gives you the actual tongue wt. of the TT you can tow without overloading.