They are similar, but smaller. I used the example of HP100's because I have a bunch of them, along with 120's and 130's. An HP80 has similar buoyancy, similar capacity and less weight than an AL80. You can remove the same 5-6 lb of lead in addition to less tank weight. You do not have to dive the same total weight of body and equipment.
You said "When you do a weight check your total body weight (body plus kit) has to be the same regardless of what tank and amount of weight you use"
The simple difference between total weight in the tropics and total weight in Canada shows this is not true.