Well, for a start, it is technically challenging.
Spinning a superconductor in the vicinity of sensitive weighing equipment has all sorts of issues. For example, I used to routinely challenge and calibrate '4' and '5' place' digital balances (0.1mg & 0.01mg sensitivities ;-) and, despite a sophisticated design developed to resist interference from draft, vibration, temperature variations, micro-tilts etc etc, weird stuff happened.
Even set on a free-standing, slate-bed balance table, with an auxiliary draft shield around a balance with motorised doors, one instrument might refuse to settle before mid-morning, though it was continuously 'on' to eliminate 'warm-up' issues. Another would wander when laden fork-lifts passed fifteen metres below. An otherwise amiable balance developed hiccups when all three 'fast' flask shakers were run in a side-room. It was their beat frequencies, we supposed...
All seemed mildly allergic to an old spectrometer which had a large transformer rather than a switching power supply, even though it was many feet away !!
The major problem with this field is, of course, the giggle factor. Too many wondrous devices have failed in the cold light of day-- Either they were out 'n' out scams, or their builder overlooked some subtle flaw. Uh, sometimes *not* so subtle, as in the case of a widget which produced a saw-tooth vibration that caused simple 'cargo' scales to read low...
I'd remind any would-be researcher of the painstaking decades spent tweaking and refining the first solar neutrino detector. Problem by problem, year by year, the operators eliminated potential sources of error. Happens the tank's detections still came up 66% short, but that eventually led to acceptance that neutrinos are *not* massless, so can 'morph' between varieties...
With out-gassing, bubbling, diminishing tank contents, leaking and wobbling bearings & seals etc etc, the cryogenics alone represent a formidable challenge to 'antigrav' experiments' sensitivity and reproducibility !!
Come the '-40' superconductors, hobbyists might get involved...