[F=mg]

[thejohnlreed]

-------When we use a balance scale to measure weight [mg] we are
making use of the quantity [g] that with respect to the balance scale
function, is a consequence of the balance scale's location in space.
The quantity [g] at the balance scale location acts uniformly on each
pan of the balance scale and on the observer, and persists as a
uniform attraction on the contents of each pan to bring the
comparative resistance quantity mass [m] to balance in the attraction
field that acts uniformly on atoms. The uniform quantity [g] at
location allows the observer to measure comparative magnitudes of non-
uniform atomic matter in conserved quantitative uniform units that the
observer feels as resistance and defines as mass [m]. The balance
scale compares the resistance of two pans of matter.

[mg]1 = [mg]2 on the balance scale where [g] divides out because it is
a uniform external to the balance scale influence on each pan.

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.