Except in the balanced field length case there is a choice of V1 from V1min to V1max.
V1 max is the accelerate/stop case and V1min is the accelerate/go case.
The reason that in tabulated V speed charts the V speed increases with increasing mass is that you must be able to accelerate from the point at which the engine fails to VR and meet the screen height at the end of the TODA.
Incidentally the first segment is from 35 feet to the end of gear retraction.