Hi,
To the best of my knowledge Vmcg does not vary with weight. However RTOW(Regulated Take off Weight) is affected by Vmcg.
Vmcg is the absolute lower limit of V1 and when you have a V1 less than Vmcg, you cannot legally take off. The solution to this problem is to simply push V1 up........but if you are limited by your stopping distance, the only way you can push V1 up is by reducing the RTOW.
This generally occurs in practice when taking off well below structural limits off very short runways(ie off a balanced field).
Hope it helps
KTK