It might, but how much weight is the question. The problem is that the down-force on each carriage changes depending on where the head is, relative to the carriage. As it moves further away from any given carriage, in the X-Y plane, it puts less down-force on the carriage.
In addition, benefits of the counterweight have to be *ahem* weighed against the additional inertia added to the system by adding the counterweights.
All that adding the counterweights will do is increase the maximum acceleration that the platform can use.
[edit: ] Provided, of course, that the counterweight inertia is less than the reclaimed downforce--now that I think about it, this can never be true, so you can't increase the maximum acceleration available by adding counterweights.
In addition, benefits of the counterweight have to be *ahem* weighed against the additional inertia added to the system by adding the counterweights.
All that adding the counterweights will do is increase the maximum acceleration that the platform can use.
[edit: ] Provided, of course, that the counterweight inertia is less than the reclaimed downforce--now that I think about it, this can never be true, so you can't increase the maximum acceleration available by adding counterweights.