If it moves the needle of a weight scale or force meter, it's a force.
But I'd say that the force that eventually moves the needle is not gravity, but the one that the table applies to the scale to prevent it from going down.
The contact camp agrees with you.
I'm in the contact camp: a scale or balance blocks the freely falling motion of the weighed item. Or, by equivalence, the weighing apparatus (and anything supporting it, be it the whole planet Earth or a rocket engine) imparts an acceleration (i.e., applies a force) on the weighed item, so the latter cannot be in geodesic motion.
The net force is zero.
When forces balance, they may balance to zero so the object in question doesn't move; but there is compression or tension in it. The scale measures that stress. If you remove either gravity or the restraining support (floor, table, ...) the stress goes away.
Force is defined as mass times acceleration: F = ma.
A body falling due to gravity experiences a force because it has mass and is accelerating. That's how force is defined.
Gravity is a pseudo force.
Centrifugal force is pseudo, but centripetal acceleration isn't.
In what reference frame can we properly understand gravitational attraction, if the obvious one is fictional?
The frame of reference is the curved 4 dimensions space-time
F = ma
But you can create a black hole by putting enough photons in one place.