  Recent weak lensing surveys have revealed that the direct measurement of the
parameter combination $S_8\equiv\sigma_8(\Omega_m/0.3)^{0.5}$ -- where
$\sigma_8$ is a measure of the amplitude of matter fluctuations on 8
$h^{-1}$Mpc scales -- is $\sim3\sigma$ discrepant with the value reconstructed
from cosmic microwave background (CMB) data assuming the $\Lambda$CDM model. In
this article, we show that it is possible to resolve the tension if dark matter
(DM) decays with a lifetime of $\Gamma^{-1} \simeq 55 \ \text{Gyrs}$ into one
massless and one massive product, and transfers a fraction $\varepsilon\simeq
0.7 \ \%$ of its rest mass energy to the massless component. The velocity-kick
received by the massive daughter leads to a suppression of gravitational
clustering below its free-streaming length, thereby reducing the $\sigma_8$
value as compared to that inferred from the standard $\Lambda$CDM model, in a
similar fashion to massive neutrino and standard warm DM. Contrarily to the
latter scenarios, the time-dependence of the power suppression and the
free-streaming scale allows the 2-body decaying DM scenario to accommodate CMB,
baryon acoustic oscillation, growth factor and un-calibrated supernova Ia data.
We briefly discuss implications for DM model building, galactic small-scale
structure problems and the recent Xenon-1T excess. Future experiments measuring
the growth factor to high accuracy at $0\lesssim z\lesssim1$ can further test
this scenario.
