The classic answer is that Vmcg is not considered to be a function of weight. But as with all things aeronautic that's a bit of a simplification.
For example, since deviation from track is the criteria for assessing Vmcg, one might expect that a significantly lighter aircraft might react so quickly to the disturbance that it exceeds the 30ft deviation, even if it were to come back towards the track just as promptly.
Also, the amount of weight carried on the gear will very much affect the tyre dynamics etc, and undercarraige forces can be an important factor.
The Vmcg reg actually calls for the "most unfavourable weight in the range of takeoff weights" so that does recognise the possibility of a weight effect, even though it's usually pretty much minor/negligible for the range one considers on a given aircraft.