  We investigate the origin of $\Lambda$CDM parameter constraints in weak
lensing, with a focus on the Hubble constant. We explain why current cosmic
shear data are sensitive to the parameter combination $S_8 \propto \sigma_8
\Omega_m^{0.5}$, improving upon previous studies through use of the halo model.
Motivated by the ongoing discrepancy in measurements of the Hubble constant
from high and low redshift, we explain why cosmic shear provides almost no
constraint on $H_0$ by showing how the lensing angular power spectrum depends
on physical length scales in the dark matter distribution. We derive parameter
constraints from galaxy lensing in KiDS and cosmic microwave background weak
lensing from Planck and SPTpol, separately and jointly, showing how
degeneracies between $\sigma_8$ and $\Omega_m$ can be broken. Using lensing to
calibrate the sound horizon measured in projection by baryon acoustic
oscillations gives $H_0 = 67.4 \pm 0.9 \; \mathrm{km} \, \mathrm{s}^{-1} \,
\mathrm{Mpc}^{-1}$, consistent with previous results from Planck and the Dark
Energy Survey. We find that a toy Euclid-like lensing survey provides only weak
constraints on the Hubble constant due to degeneracies with other parameters
that affect the shape of the lensing correlation functions. If external priors
on $n_s$, the baryon density, and the amplitude of baryon feedback are
available then sub-percent $H_0$ constraints are achievable with forthcoming
lensing surveys.
