  We present weak lensing constraints on the ellipticity of galaxy-scale matter
haloes and the galaxy-halo misalignment. Using data from the
Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS), we measure the
weighted-average ratio of the aligned projected ellipticity components of
galaxy matter haloes and their embedded galaxies, $f_\mathrm{h}$, split by
galaxy type. We then compare our observations to measurements taken from the
Millennium Simulation, assuming different models of galaxy-halo misalignment.
Using the Millennium Simulation we verify that the statistical estimator used
removes contamination from cosmic shear. We also detect an additional signal in
the simulation, which we interpret as the impact of intrinsic shape-shear
alignments between the lenses and their large-scale structure environment.
These alignments are likely to have caused some of the previous observational
constraints on $f_\mathrm{h}$ to be biased high. From CFHTLenS we find
$f_\mathrm{h}=-0.04 \pm 0.25$ for early-type galaxies, which is consistent with
current models for the galaxy-halo misalignment predicting $f_\mathrm{h}\simeq
0.20$. For late-type galaxies we measure $f_\mathrm{h}=0.69_{-0.36}^{+0.37}$
from CFHTLenS. This can be compared to the simulated results which yield
$f_\mathrm{h}\simeq 0.02$ for misaligned late-type models.
