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For me, it is because there is no satisfactory operational way to
determine whether or not you are in a so-called "inertial
frame."
This is because I want weight to be tied to the gravitational
(i.e., net
inertial) force as measured in a frame in which the object is not
accelerating. That force is equal in magnitude to the net
*non*gravitational force which is often easier to determine.