Why bother deriving mass ?.
All you need to know is that the acceleration is adequate to achieve V1 and have room to stop within the available distance.
All you need is an accelerometer and a database of runway lenths.
It would be a good idea to take the runway lenth from precision GPS which would cater for cases of wrong runway, intersection and taxiway foulups.
One cheap and simple piece of technology neatly covering all of the major risks with no need for error prone pilot inputs.
If the magic box yells ABORT you obey and figure out why before trying again. The cause might be overweight but there are many other potential causes, all covered.
Always remember the KISS principle - Keep It Simple Stupid.