Let me just interject that perhaps Brian is insisting on the conceptual
difference between gravitational mass and inertial mass.
The usual balance/scale measures gravitational mass and needs a non-zero
applied gravitational field to operate. Inertial mass (as in F=ma) is
directly measured by applying the same unbalanced force to the standard
and specimen masses (eg., using the 3rd law and a spring) and comparing
the resulting non-zero accelerations.
If the numerical equivalence of gravitational/inertial masses is agreed
upon, this is a moot question.