It does matter.

Not with arbitrary convention, no. That's arbitrary - of course! It has no bearing on manifest reality.

You're suggesting that objects are being pushed down due to their weight, which means that they'd be being pushed from above.

That's partially correct; they are being pushed down from above - by the weight of the matter above them (though it isn't quite that simple because they are also surrounded by matter with weight as well) - but the force of their measured weight (what i call effective weight - weight with the buoyant force i.e. as measured on a scale) principally comes from the weight of the object itself, as well as the interplay of that objects weight and the weight of the media it displaces.

Objects are built of pieces. Although their effective weight is largely influenced by their volumetric density (the volume of media those pieces collectively displace), their intrinsic weight comes from the matter they are comprised of. Weight is an intrinsic and inexorable property of all matter.

Again, objects are comprised of pieces. Each one of those pieces has weight. If it is more consistent with your arbitrary convention of "force must always push from behind" and/or helps you to understand, you may think of each piece pushing on each other in the object "pushing from behind" and cumulatively being the force that "pushes the scale from behind", to use your wacky parlance.

The question then is, what is it that's pushing down on an object from above?

Matter [its weight]! (for us on the surface of earth, typically air)

But that is only a small percentage of what pushes on the scale. Primarily it is the object's weight which pushes on the scale.

It does matter.

Not with arbitrary convention, no. That's arbitrary - of course! It has no bearing on manifest reality.

You're suggesting that objects are being pushed down due to their weight, which means that they'd be being pushed from above.

That's somewhat correct; they are being pushed down from above - by the weight of the matter above them (though it isn't quite that simple because they are also surrounded by matter with weight as well) - but the force of their measured weight (what i call effective weight - weight with the buoyant force i.e. as measured on a scale) principally comes from the weight of the object itself, as well as the interplay of that objects weight and the weight of the media it displaces.

Objects are built of pieces. Although their effective weight is largely influenced by their volumetric density (the volume of media those pieces collectively displace), their intrinsic weight comes from the matter they are comprised of. Weight is an intrinsic and inexorable property of all matter.

Again, objects are comprised of pieces. Each one of those pieces has weight. If it is more consistent with your arbitrary convention of "force must always push from behind"/ helps you to understand you may think of each piece pushing on each other in the object "pushing from behind" and cumulatively being the force that "pushes the scale from behind", to use your wacky parlance.

The question then is, what is it that's pushing down on an object from above?

Matter [its weight]! (for us on the surface of earth, typically air)

But that is only a small percentage of what pushes on the scale. Primarily it is the object's weight which pushes on the scale.