Except that clearly isn't it, as the weight moves even if there is no 'ground' (say at altitude) in the same predictable fashion, until it collides with something - which merely attempts to arrest it's movement. In fact, in orbit the forces felt are still (quite clearly) there too.

So if anything, gravity wise 'pushing' is not a property of gravity at all. Merely of matter which happens to produce the spacetime distortions which result in gravity. Unless dark matter exists, which would be neat.

Or the moon wouldn't continue to be up there, instead of 'down here'.

And clouds of hydrogen atoms will eventually collect together in a vacuum barring other outside gravitational influences. Which is notably why we even have a star.

And the weight itself also has measurable (albeit extremely tiny) such effects on everything else too.

So how do you model/name/account for that force which causes that to occur? Since it does clearly exist.

Because a rocket doesn't just 'push' either. We can clearly model the chemical and physics behaviors going on there to generate that 'push', and all involve forces which we can account for. None of them meaningfully appear to be gravity.

And gravity also involve forces (spacetime distortions causing very real effects!). Which we can also account for.

So seriously, what are you even talking about?