  We describe a dispersive Faraday optical probe of atomic spin which performs
a weak measurement of spin projection of a quantum gas continuously for more
than one second. To date focusing bright far-off-resonance probes onto quantum
gases has proved invasive, due to strong scalar and vector light shifts
exerting dipole and Stern-Gerlach forces. We show that tuning the probe near
the magic-zero wavelength at 790 nm between the fine-structure doublet of
$^{87}$Rb cancels the scalar light shift, and careful control of polarization
eliminates the vector light shift. Faraday rotations due to each fine-structure
line reinforce at this wavelength, enhancing the signal-to-noise ratio for a
fixed rate of probe-induced decoherence. Using this minimally-invasive spin
probe we perform microscale atomic magnetometry at high temporal resolution.
Spectrogram analysis of the Larmor precession signal of a single spinor
Bose-Einstein condensate measures a time-varying magnetic field strength with 1
{\mu}G accuracy every 5 ms; or equivalently makes > 200 successive measurements
each at $10\,\mathrm{pT/\sqrt{Hz}}$ sensitivity.
