Mutt, what utter nonsense
Reducing TOM will not have any effect!!!!!
First decrease TOM, and V1 will increase, I needs to reach Vmcg at least.
It says Balanced Field, this means TODA = ASDA, the whole point of a balanced field is to give you the best chance either way,
A balanced field takeoff is a condition where the accelerate-stop distance required (ASDR) is equal to the takeoff distance required (TODR) for the aircraft weight, engine thrust, aircraft configuration and runway condition
If A was correct, how could increasing V1 reduce the TODR?
Vr will still happen at the same speed, providing conditions are the same!
Reducing your weight would let you accelerate faster, ergo you would be able to reach a higher V1, less weight will also give you less inertia, so you can stop faster!