  Self--interactions of dark matter particles impact the distribution of dark
matter in halos. The exact nature of the self--interactions can lead to either
expansion or collapse of the core within the halo lifetime, leaving distinctive
signatures in the dark matter distributions not only at the halo center but
throughout the virial region. Optical galaxy surveys, which precisely measure
the weak lensing of background galaxies by massive foreground clusters, allow
us to directly measure the matter distribution within clusters and probe subtle
effects of self--interacting dark matter (SIDM) throughout the halo's full
radial range. We compare the weak--lensing measurements reported by Shin et al.
2021, which use lens clusters identified by the Atacama Cosmology Telescope
Survey and source galaxies from the Dark Energy Survey, with predictions from
SIDM models having either elastic or dissipative self--interactions. To model
the weak--lensing observables, we use cosmological N-body simulations for
elastic self--interactions and semi-analytical fluid simulations for
dissipative self--interactions. We find that current weak--lensing measurements
already constrain the isotropic and elastic SIDM to a cross-section per mass of
$\sigma/m<1~{\rm cm^2/g}$ at a $95\%$ confidence level. The same measurements
also impose novel constraints on the energy loss per unit mass for dissipative
SIDM. Upcoming surveys are anticipated to enhance the signal-to-noise of
weak--lensing observables significantly making them effective tools for
investigating the nature of dark matter, including self--interactions, through
weak lensing.
