Marek (Actusreus), as an electrical person I'll offer an electrical hypothesis :-)
If, as you suspect, magnetic effects are not the cause, one guess is that the electronic circuitry in the gauge is being affected by either stray capacitance between its various circuit points and the tonearm/headshell/cartridge assembly or the wiring it contains, or by low-level EMI/RFI being emitted from that assembly.
Sensitivity to those kinds of effects could very conceivably vary as a function of battery strength (consistent with Phil's observation). It could also be expected to vary unpredictably during the tonearm's descent, as the angular alignment and the distance between the gauge's circuitry and the tonearm/headshell/cartridge changes.
Alternatively, it could be that digital noise generated by the gauge's circuitry is radiating through its display window (the one part of the gauge that appears to be electrically unshielded across a significant area) into the tonearm/headshell/cartridge assembly, and radiating or capacitively coupling from there through the air into the metallic structure that the stylus is being lowered onto. From there the noise would re-enter the gauge's circuitry, coupling into different circuit points than those from which it originated, again with unpredictable effects.
These kinds of effects could perhaps be viewed as electrical counterparts to the kinds of mechanical effects Doug was referring to in his comment that "ANY scale that resolves to .01g or better will respond to the slightest changes in air currents. I can alter the reading on my scale (different brand, same resolution) by waving my hand over it." :-)
Best regards,
-- Al