  Galaxies are biased tracers of the matter density on cosmological scales. For
future tests of galaxy models, we refine and assess a method to measure galaxy
biasing as function of physical scale $k$ with weak gravitational lensing. This
method enables us to reconstruct the galaxy bias factor $b(k)$ as well as the
galaxy-matter correlation $r(k)$ on spatial scales between $0.01\,h\,{\rm
Mpc^{-1}}\lesssim k\lesssim10\,h\,{\rm
  Mpc^{-1}}$ for redshift-binned lens galaxies below redshift $z\lesssim0.6$.
In the refinement, we account for an intrinsic alignment of source
ellipticities, and we correct for the magnification bias of the lens galaxies,
relevant for the galaxy-galaxy lensing signal, to improve the accuracy of the
reconstructed $r(k)$. For simulated data, the reconstructions achieve an
accuracy of $3-7\%$ (68\% confidence level) over the above $k$-range for a
survey area and a typical depth of contemporary ground-based surveys.
Realistically the accuracy is, however, probably reduced to about $10-15\%$,
mainly by systematic uncertainties in the assumed intrinsic source alignment,
the fiducial cosmology, and the redshift distributions of lens and source
galaxies (in that order). Furthermore, our reconstruction technique employs
physical templates for $b(k)$ and $r(k)$ that elucidate the impact of central
galaxies and the halo-occupation statistics of satellite galaxies on the
scale-dependence of galaxy bias, which we discuss in the paper. In a first
demonstration, we apply this method to previous measurements in the
Garching-Bonn-Deep Survey and give a physical interpretation of the lens
population.
