To answer your questions, all that is needed is to have a quick look at the definitions of Vmcg/Vmca....
Vmcg on the ground is the minimum speed during the TKOF run, at which when a critical engine suffers total pwr loss, it is possible to maintain directional control of the aeroplane with
only the use of aerodynamic controls and enable the TKOF to
continue safely. For this reason V1 must be equal of greater then Vmcg. Therefore V1 is where your weight comes into the equation.... not Vmcg.
Vmca is the minimum flight speed at which the aeroplane can be directionally controlled without the loss of height if the critical engine fails with all remaining engines at TKOF thrust. It is calculated using
maximum BRW with the most adverse CoG, gear fully retracted, the flaps at TKOF setting and with the optimum bank angle towards the operating engine/s ( typically 3-5 degrees).
So to answer your questions.... Vmcg is not directly effected by weight because V1 is. Vmca is based on your max weight already and Vmcg is usually faster then Vmca because you do not have the added aerodynamic benefit of bank into the live engine/s on the ground.
Hope that helps
