  We present a novel approach to extracting dwarf galaxies from photometric
data to measure their average halo mass profile with weak lensing. We
characterise their stellar mass and redshift distributions with a spectroscopic
calibration sample. Using the ${\sim}5000\mathrm{deg}^2$ multi-band photometry
from Dark Energy Survey and redshifts from the Satellites Around Galactic
Analogs (SAGA) survey with an unsupervised machine learning method, we select a
low-mass galaxy sample spanning redshifts $z{<}0.3$ and divide it into three
mass bins. From low to high median mass, the bins contain [146 420, 330 146,
275 028] galaxies and have median stellar masses of $\log_{10}(M_*/M_{\odot})=
[8.52^{+0.57}_{-0.76}, 9.02^{+0.50}_ {-0.64}, 9.49^{+0.50}_{-0.58}]$. We
measure the stacked excess surface mass density profiles, $\Delta\Sigma(R)$, of
these galaxies using galaxy--galaxy lensing with a signal-to-noise of [14, 23,
28]. Through a simulation-based forward-modelling approach, we fit the
measurements to constrain the stellar-to-halo mass relation and find the median
halo mass of these samples to be $\log_{10}(M_{\rm halo}/M_{\odot})$ =
[$10.67\substack{+0.2\\-0.4}$, $11.01\substack{+0.14 \\
-0.27}$,$11.40\substack{+0.08\\-0.15}$]. The CDM profiles are consistent with
NFW profiles over scales ${\lesssim}0.15 \rm{h}^{-1}$Mpc. We find that
${\sim}20$ per cent of the dwarf galaxy sample are satellites. This is the
first measurement of the halo profiles and masses of such a comprehensive,
low-mass galaxy sample. The techniques presented here pave the way for
extracting and analysing even lower-mass dwarf galaxies and for more finely
splitting galaxies by their properties with future photometric and
spectroscopic survey data.
