You'd have to go a hell of a long way from Earth to be even close to truly "weightless,"

Well now. The ISS achieves something that you cannot gainsay, because whatever you argue, the error will be unmeasurable, by you. And most people. And while we are being pedantic, and measuring our weight in ato-Newtons, could we point out that Earth's pull on orbiting objects varies around the circumferencial because of mascons eg around Hawaii. The alleged thing that slammed into us and produced the Moon, it is postulated, left a denser lump of mass in the Earth. NASA knew to calculate for this very early on. Earth is not a sphere per se, nor a perfect oblate spheroid.