What is V1? It's the speed at which you either act to abort the takeoff by applying brakes or reducing power, or it's the speed at which you do nothing and continue with the takeoff. If you do nothing at V1, how does it affect the accelerate-go distance? It doesn't. It's the speed at which you rotate that will affect the accelerate-go distance.
It does actually. Lower the decision speed is, the higher the distance to Vr in ef case is, since you are accelerating on one less engine for more.
As such, V1go increases as mass increases, it might or might not increase past Vmcg, and it might or might not influence V1min.
As for the original question, I can only imagine that by putting more pressure on tyres, the lateral resistance/friction increases helping steering effectiveness.