  The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the
expansion rate of the universe so its precise measurement is important to
understand the fundamental dynamics of our evolving universe. One of the major
limitations of measuring $H_0$ using time-delay cosmography is the presence of
the mass-sheet degeneracy (MSD) in the lens mass modeling. We propose and
quantitatively assess the use of galaxy-galaxy shear measurements to break the
MSD in the strong lensing mass modeling. We use stacked galaxy-galaxy lensing
profiles and corresponding covariance matrices from Huang et al. (2022) to
constrain the MSD in lens mass modeling with a highly flexible mass profile.
Our analyses show that if ideally all galaxy-galaxy lensing measurements from
the Hyper Suprime-Cam (HSC) survey can be used to constrain the MSD, we can
achieve $\sim 10\%$ precision on the MSD constraint. We forecast that
galaxy-galaxy lensing measurements from LSST-like surveys can in general
constrain the MSD with $\sim 1-3\%$ precision. Furthermore, if we push weak
lensing measurements to a lower angular scale of $\sim 0.04$ $\rm Mpc$, a
survey like LSST can provide $\sim 1\%$ precision on the MSD constraint,
enabling a measurement of $H_0$ at the $1\%$ level. We demonstrate that
galaxy-galaxy weak lensing can robustly constrain the MSD independent of
stellar kinematics of the deflector, with wide-field survey data alone.
