We present an analytical calculation of the probability distribution of the magnification of distant sources due to weak gravitational lensing from non-linear scales, using a realistic description of the non-linear density field. Then, we can directly express the p.d.f. $P(\mu)$ in terms of the p.d.f. of the density contrast realized on non-linear scales (typical of galaxies). Next, we study the effects of weak lensing on the derivation of the cosmological parameters from SNeIa. We show that the inaccuracy introduced by weak lensing is rather small and that observations can unambiguously discriminate between $\Omega_m=0.3$ and $\Omega_m=1$, and one can clearly distinguish an open model from a flat cosmology. However, we note that going to high redshift $z_s >1$ does not decrease much the inaccuracy because weak lensing effects grow with $z_s$. On the other hand, one may obtain some valuable information on the properties of the underlying non-linear density field from the measure of weak lensing distortions.

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