Does a person weigh less when falling?

Yeah, I remember that satellite design. One of the Gravity Probes? (googling isn’t helping).

What do people think of the opposite question - do people weigh more when accelerating? I’d say yes - whether the deviation from free-fall is because the attractive force of Earth is being resisted by the ground, or because the rocket motor is pushing upwards causing with five gees of acceleration, weight is what the spring scale says.

Isn’t this one of the fundamental tenets of general relativity - that an accelerating frame of reference is indistinguishable from a gravity field?

Yes. In the limit of a small enough hypervolume of space-time, gravity is indistinguishable from acceleration

Yeah, Gravity Probe B is the one I was thinking of:

I think there are other examples, but this was one of the most accurate.

Thanks. Here’s an explicit mention of how drag was eliminated

The translation control system used acceleration measurements from one science gyroscope’s suspension system to null out the effects of external forces from the on-orbit environment (solar wind, radiation pressure, etc). In this way, the vehicle was controlled to fly in a near-perfect gravitational orbit; transverse accelerations on the science gyroscopes were reduced to the 5x10-12 g level.

I found this older document as well:
The Drag-Free Satellite

A scientific earth satellite that is guided in a drag -free orbit by a shielded, free-falling proof mass has been proposed by a number of investigators. This paper examines the feasibility and some of the applications of this scheme. The control and guidance system is analyzed with respect to system performance and gas usage requirements. The principal trajectory errors that are due to vehicle gravity, stray electric and magnetic fields, and sensor forces are investigated. I t is found that drag and solar radiation pressure forces may be effectively reduced by three to five orders of magnitude for 100- to 500-mile orbits and that the deviation from a purely -gravitational orbit may be made as small as 1 m/yr. Such a satellite could be used to make precise measurements in geodesy and aeronomy; and, if a spherical proof mass is spun as a gyroscope, its random drift rate would probably be less than 0.1 sec-arc/yr. Such a gyroscope could be used to measure the effects that would ultimately limit the performance of the best terrestrial or satellite-borne gyros, and it might also be good enough to perform the experiment proposed by G. E. Pugh and L. I. Schiff to test general relativity.

It’s from 1964 (and it seems the ideas were “in the air” for longer than that). It proposes the same test of General Relativity that Gravity Probe B performed.

Thanks. The NASA history of GP-B says it started funding studies about how to test GR in 1961

https://einstein.stanford.edu/MISSION/mission2.html

One of the many important discussions that took place during the 1961 Stanford conference on testing relativity was the need for a drag-compensated satellite—that is, a satellite that could orbit the Earth in a state of free fall, with no drag or resistance from the atmosphere or solar radiation pressure. Among the conference attendees were two of Cannon’s graduate students: Daniel DeBra, who was finishing his Ph.D. while heading up the Dynamics & Controls Analysis Group at Lockheed Missiles & Space Company (now Lockheed Martin Space Systems Company, abbreviated hereon as “LM”), and Benjamin Lange, also from LM, who was just starting his graduate studies in the Stanford Aero-Astro Department.