alpine pilot:
Yes you can operate balanced when V1=VR, BUT only if VR is reduced to V1. If V1 is increased ASDR will be longer than TODR and therefor the TO will be unbalanced.
Sometimes , very very heavy or very very light aircraft, V1 must be reduced or increased to comply with Vmcg, Vmbe restrictions, in this scenario V1 might equal VR BUT won´t be a balanced take off.
In a long runway does not make sense to reduced V1, What for?
Regarding taking off from a contaminated runway, YES it can happen that your RTOM or OTOW (however you call it) might be higher if the deposit is deeper. WHY? Consider that if this deposit is a fluid contaminant( slush, loose snow) it will decrease the braking performance but also will increase the precipitation drag( displacement and spray impigment drag). So as your max take off weight will be a "trade off" between the accelerate go and accelerate stop, with a bigger drag you may find out higher weights when the depht of the deposit is higher.