The stone may drop to the ground, it certainly dosen't have to, it certainly isn't a physical constant.
It certainly has to, darkbeaver. Gravitational pull of the earth is a physical constant; there is nothing metaphysical about gravitation (as you will easily find out if you try to walk out of a window on tenth floor).
The weight of the stone determines weather it goes up down or sideways Joe.
It is not the weight which determines that, it is the density. Take a gravel particle weighing one gram, and a sheet of paper weighing ten grams. Gravel will drop to the ground; sheet of paper will float on the air, due to the wind. It is not the weight, but density (and surface area) that is important.
And density of stone is always much more than anything that can be carried away by the wind. We don’t have wind fast enough on earth, to carry away a stone.
And suppose there actually arose a wind of that proportions (hundreds or thousands of miles per hour, I don’t know), then the experiment of going outdoors and dropping the stone will be totally impossible to carry out anyway. So the question does not arise.
The weight varies from local to local. Stone can go up pretty easily in the right conditions
Sure weight can vary, but as I said, it is the density that is important, density of stone does not vary much, it is always much higher than that of water. And no, the stone can never go up, not on earth, not anywhere else (though it may come down very slowly on some of the smaller asteroids).
No, I don’t’ think you can find even one instance of violation of the absolute. Go outdoors anywhere on earth, pick up a stone from the ground, drop it from one meter height, it will drop to the ground. I cannot conceive of any exception to this.