[Anthony]

Realistically, I suspect case weight is more a function of propellant weight than projectile weight. If you've got a 4g bullet with 1.5g powder (5.56mm), the powder is something like three times the volume of the bullet and is enclosed completely while the bullet is only partially enclosed, so ~90% of the case volume is for powder. On the other hand, if you've got a 7.5g bullet with 0.3 grams of powder (9mm), something like 40% of the case is for powder, and it's at lower pressure so the case walls can be thinner.