Tarik,(ssg)
Whenever you are not at the runway limited max take off weight there will be a range of v1 speeds available.
Think of the lowest v1 as the lowest speed you could safely continue the take off after an engine failure and the highest v1 as the highest speed from which you can stop.
Some one decides on a policy of which speed to use and you use it. It may be that the decision is to use "Balanced" speeds in which case if the engine failure occurs at the exact Vef speed used in the calculation then the distance to continue to screen height would be the same as the distance taken to stop.
For all other v1s the distances required are unequal.
Your question about different speeds at different weights makes no sense! Now if you were to ask why can't i stop after a V1min of 119 when the V1max at the same weight is 150 then that would make for an interesting discussion.
as it is you need to study the concept a little more then get back to us.