  Decaying dark matter (DDM) scenarios have recently regained attention due to
their potential ability to resolve the well-known clustering (or $S_8$) tension
between weak lensing (WL) and cosmic microwave background (CMB) measurements.
In this paper, we investigate a well-established model where the original dark
matter particle decays into a massless particle and a massive daughter
particle. The latter obtains a velocity kick during the decay process that
results in the suppression of the matter power spectrum at scales that are
observable with WL shear observations. We perform the first fully non-linear WL
analysis of this two-body decaying dark matter ($\Lambda$DDM) scenario,
including intrinsic alignment and baryonic feedback processes. We used the
cosmic shear band power spectra from \textit{KiDS-1000} data and combined it
with temperature and polarisation data from \texttt{Planck} in order to
constrain the $\Lambda$DDM model. We report new limits on the decay rate and
mass splitting parameters that are significantly stronger than previous
results, especially in the case of low-mass splittings. Regarding the $S_8$
tension, we found a reduction from about 3 to 2 $\sigma$, depending on which
statistical measure is applied. We therefore conclude that the two-body
$\Lambda$DDM model is able to reduce the $S_8$ tension without convincingly
solving it.
