i've weighed thousands of cases and never found US military 5.56mm cases to be thicker/heavier than US commercial .223 cases.
This has been my experience also.
A few things should be kept in mind when over thinking this issue. One is that you have to trim the cases before weighing them so there is some uniformity to begin with. Another is that the difference between chambers is very likely talking about bolt action rifles in 223 vs semi autos in 223/5.56.
My AR eats any brass, my M1A eats any brass. All my ammo is handloads excepting the occasional surplus military ammo. I wont shoot commercial 308 Win ammo through my M1A.