There are several satellites that study the atmosphere. There is even a satellite dedicated to polar regions. There are also several land-based radar arrays studying the poles (I am good friends with some scientists who work with these arrays). Finally, since 1998 commercial flights have flown directly over the North Pole.
Somehow none of these have noticed a 50% change in air density. Air density is a vital parameter for over-the-horizon radar, and obviously very important to aircraft.
Technically, of course, even Captain Byrd's testimony (and by that, I mean ``what some kid remembered hearing Capt. Byrd say on the radio, even though nobody else does'') doesn't suggest that there was a 50% change in air density. Somehow you have extrapolated the claims that Capt. Byrd saw verdant fields over the pole (or hallucinated the fields) as proof that there was a 2g anomalous gravity field.
If Capt. Byrd had said (or had been reported to say) ``Holy #$#%! My plane is suddenly falling from the sky like a rock, even though all flight systems are working fine!'' before crashing, that might be extrapolated to suggesting an anomalous gravity field.
Neither you, nor I, nor anyone without detailed knowledge of the actual equipment setup for Gravity Probe B would know what to do with the original data. What is wrong with the data in Figure 7?
And apparently the air above this dome was unperturbed, since the good pilots did not report any sudden turbulence? (Not to mention the fact that the only pilot to go on record stating his name and his observations did not claim that the water bubble was 3000 feet tall, only that it was broad enough for JFK airport (Idlewild was the old name for JFK, so I assume that is what the pilot meant) could fit within it easily.)