Normally, if discussing whether something varies with a parameter, the assumption is that all other parameters are held constant.
So the question, "Does VMCA/VMCG vary with weight?" has the implied additional "assuming all other relevant parameters are held constant".
This is possible to do if you assume some form of ballast control, as is present on most flight test aircraft.
If we now consider this version of the question, and split it into two (we'll see why soon):
"Does VMCA vary with weight?"
The answer is, yes it does. For most aircraft there is a declared VMCA, and this may be a single declared value. The underlying "real" VMCA is, however, very much a function of weight, and there are also some (recent) aircraft where it is explicitly declared to be a function of weight (The Embraer E-Jets make such a declaration, I believe).
The reason it is a function of weight is the way that VMCA is determined; for the steady state case, the aircraft may be banked up to 5 degrees in a favourable direction. This allows some small additional sideslip to be present (so that aerodynamic sideforce is opposing the weight component in the lateral direction). This sideslip helps to counter the yawing moment caused by the engine asymmetry. The bigger the sideslip, the more it helps. The heavier the aircraft, the bigger the lateral weight component, and so the bigger the sideslip.
So a heavier aircraft, if flown to the VMCA test rules, will have a lower value of VMCA if all other factors are constant.
"Does VMCG vary with weight?"
The answer to this one is, basically, "no". Again we have to be careful about secondary effects through other parameters, but if they are controlled then there is little effect of weight. This is because the determination of VMCG is done in a fashion that no direct weight effect is available to assist.