The chart that you are looking at is a V1=V1MCG limit chart, therefore V1 does play a role in the weight calculation.
For a greater depth of contaminant you will get a higher takeoff weight due to the "ploughing" effect encountered during the stop, this aids the aircraft in stopping and allows the V1 to be increased, the higher V1 permits a higher limiting weight.
If you are still in doubt, ask your training people to show you the Boeing presetation on the subject.
Mutt