To clarify, the only speed that varies for a given weight is V1.
Where I work we have tabulated performance data for the runways we operate from. We go into the charts using the current ambient conditions, including flex temperature if applicable, and find out what take-off weight can be used with those conditions. The weight in the chart has a V1 that applies to that runway and that weight. Provided our actual weight is lower than the chart weight, we use Vr, V2, Vfto, and Ver speeds from the speed card for our actual weight. V1 is the lower of the number from the RTOW tables or Vr. Sometimes there is a split between V1 and Vr sometimes they are the same. There is only a significant split on a short, wet runway with minimal obstacles in the departure path.
Assuming we can take the same weight from full length or an intersection, the only variation may be in the V1, all other speeds come from the card.