Weight is a factor in determining the "minimum control speed" for the specific conditions in question, because the higher the weight, the larger the sideforce which results from the 5 deg bank into the live engine, and thus the larger the sideslip which can be generated. This sideslip aids directional control, so the heavier aircraft can achieve a lower speed, all other factors being equal.
Traditionally, the declared Vmca has been a single value, independent of weight, and thus the value obtained at minimum flight weight is declared. Thus, for those aircraft the declared Vmca does not vary with weight, even though the underlying behaviour of the aircraft does vary. Recently, some aircraft have declared a range of Vmca as a function of weight to reflect the underlying controllability limits; the Embraer 190 does this, I believe.