[mg]1 = [mg]2 on the balance scale where [g] divides out because it is
a uniform external to the balance scale influence.
The balance scale compares at any location [g] the resistance [m] of
the non-uniform pans of atomic matter. The observer feels the product
[mg] at location [g]. The observer views the conserved comparative
resistance [m] at any location, as a partial causal factor of the
variable location product, weight [mg], that the observer feels.
This is a sound conclusion.
The observer also concludes that the weight [mg] is equal and opposite
to a force the observer applies and feels [F=mg]. This is not a sound
conclusion. The quantity [mg] is a resistance that is equal to a force
the observer applies [F=mg]. This is a sound conclusion.
The math works either way.