To use easy numbers, assume a real "tank" is 16ft x 16ft x 16ft. = 4096 cu ft
The 1/16 model would be 1ft x 1ft x 1ft = 1 cu ft.

Assume density is not scaled (a piece of aluminum at full scale is the same density as a piece of aluminum used in a model).

Then if the 4096 cu ft of the real "tank" weighs 25 tons (50,000 lbs), then the 1 cu ft of the scale tank would be :

50,000 lbs per 4096 cu ft = 12.2 lbs per 1 cu ft.

So a 25 ton tank at1/16 scale is 12.2 lbs.

My King Tiger, metal tracks, big batts, metal gearbox, big motors, etc weighs 14lbs. Not far off.

(It doesn't matter what tank dimensions you use, but each linear dimension has to be divided by 16 before the volume of the 1/16 model tank is calculated)

(Blackcat has the sameanswer presented a little diffeently)