Sonia767,
This is one of those classic cases where thinking about someting too much...or questioning something too much is counterproductive.
V1 is a 'derived' speed, based on many variables one of which is weight.
Some days on long runways at light weights it is clearly possible to stop successfully beyond V1...BUT WE DONT unless something dramatically more disastrous than a fire or failure occurrs....both of which are, performance wise, 'non events'. To do otherwise is to invite a multitude of personal variations on when it's Ok to stop and when it's not...far, FAR too subjective and the very reason why smart men came up Perf A/FAR 25/CAO 20.7.1b back in the 50s...to stop needless crashes caused by "But I thought I could stop"..or "I thought it would clear the trees"
Please accept also that V1 is NOT 'Decision speed' but 'decision made speed'. Or a 'first braking aid applied' speed.
In the 'runway limited' case your 'decision speed' is more like V1-5-10kts because inertia will take you beyond V1 even after a sudden and complete power loss...particularly the fire case which may have no significant associated power/thrust loss.
When you have a balanced field the actual stopping bit is balanced on a knife edge...I'm sure during CRM Initial years ago we were told rejected takeoffs were the least well understood and most likely accident scenario of all.
Chuck.