We study the dissipative effects of baryon physics on cosmic statistics at small scales using a cosmological simulation of a (50Mpch-1)3 volume of universe. The MareNostrum simulation was performed using the adaptive mesh refinement (AMR) code RAMSES, and includes most of the physical ingredients which are part of the current theory of galaxy formation, such as metal-dependent cooling and UV heating, subgrid modelling of the interstellar medium, star formation and supernova feedback. We reran the same initial conditions for a dark matter only universe, as a reference point for baryon-free cosmic statistics. In this paper, we present the measured small-scale amplification of σ2 and S3 due to baryonic physics and their interpretation in the framework of the halo model. As shown in recent studies, the effect of baryons on the matter power spectrum can be accounted for at scales k <~ 10hMpc-1 by modifying the halo concentration parameter. We propose to extend this result by using a composite halo profile, which is a linear combination of a Navarro, Frenk and White profile for the dark matter component and an exponential disc profile mimicking the baryonic component at the heart of the halo. This halo profile form is physically motivated and depends on two parameters, the mass fraction f d of baryons in the disc and the ratio λd of the disc's characteristic scale to the halo's virial radius. We find this composite profile to reproduce both the small-scale variance and skewness boosts measured in the simulation up to k ~ 102hMpc-1 for physically meaningful values of the parameters f d and λd. Although simulations like the one presented here usually suffer from various problems when compared to observations, our modified halo model could be used as a fitting model to improve the determination of cosmological parameters from weak lensing convergence spectra and skewness measurements.