Different factors require different amounts of runway length. Or another way, different factors allow different weights for a given runway length. One of those factors will be more limiting than the others. This critical factor will be the one that determines the length needed (or weight available for the length). That means that there is some 'spare' weight capacity available & waiting to be used in all the other factors provided the critical factor can be adjusted so that it is not so limiting.
If Vmcg is the most critical - limiting - factor (by setting the min V1/Vr ) then reducing it reduces the amount of runway required. That lets one add additional weight until it or some other factor becomes limiting again.
In the example above the thrust to get airborne doesn't seem to be the problem. Instead Vmcg causes a limit so altering that factor gives a bit more margin to use for more weight.
That's my understanding...
