Of course, this falls apart up close to the surface of the earth. Although we can measure a six-foot ascent of an instrument, the instrument does not prove Newton's law. Because obviously the square of the distance of a person two feet above the earth, and a person four feet above the earth will not follow that law. Or else everyone would weigh their packages for shipping on the top floor of the empire state building.
Newton's law of gravity kind of works as a vague reference to get you into the ballpark. It is just an obscure reference.
The reason is that gravity, like all forces in our universe, is a pushing force. There are no forces of attraction, only apparent forces of attraction. As ambient radiation, which travels through all matter, from all directions in the universe, moves from one substance to another, its velocity is altered. If that ambient radiation were carrying light, it would impart light on the object it strikes, sunlight, starlight, whatever light it is communicating.
Near the surface of heavenly bodies, there is a bottleneck of ambient radiation as it changes velocity at the surface of the planet, star, or the sun. Like automobile traffic backs up, so does ambient radiation as it approaches the surface of a heavenly body. As it slows from totally undetectable velocity, it imparts force upon objects near the bottleneck; that force, the pressure, is gravity.