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You forgot to specify, (I am not criticizing you for this) that the
acceleration is "in our so-called inertial frame of reference". Some
want to make a central issues out of it, others prefer to focus on
differences between v and a, or between mass and weight. Unfortunately,
many students have difficulties with these things. That is the issue.
Some said we need a new noun, microgravity, others said that the one
we already use, apparent weight, is good enough for the purpose of
dealing with a specific activity in a specific elevator using a specific
forcemeter.