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 $zin[0.1,,0.6]$. 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.
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