  We present a cosmological analysis of abundances and stacked weak-lensing
profiles of galaxy clusters, exploiting the AMICO KiDS-DR3 catalogue. The
sample consists of 3652 galaxy clusters with intrinsic richness
$\lambda^*\geq20$, over an effective area of 377 deg$^2$, in the redshift range
$z\in[0.1,\,0.6]$. We quantified the purity and completeness of the sample
through simulations. The statistical analysis has been performed by
simultaneously modelling the comoving number density of galaxy clusters and the
scaling relation between the intrinsic richnesses and the cluster masses,
assessed through a stacked weak-lensing profile modelling. The fluctuations of
the matter background density, caused by super-survey modes, have been taken
into account in the likelihood. Assuming a flat $\Lambda$CDM model, we
constrained $\Omega_{\rm m}$, $\sigma_8$, $S_8 \equiv \sigma_8(\Omega_{\rm
m}/0.3)^{0.5}$, and the parameters of the mass-richness scaling relation. We
obtained $\Omega_{\rm m}=0.24^{+0.04}_{-0.03}$,
$\sigma_8=0.89^{+0.06}_{-0.05}$, $S_8=0.80^{+0.04}_{-0.04}$. The constraint on
$S_8$ is consistent within 1$\sigma$ with the results from WMAP and Planck.
Furthermore, we got constraints on the cluster mass scaling relation in
agreement with those obtained from a previous weak-lensing only analysis.
