  As pointed out in previous studies, the measurement of the skewness of the
convergence field $\kappa$ will be useful in breaking the degeneracy among the
cosmological parameters constrained from weak lensing observations. The
combination of shot noise and finite survey volume implies that such a
measurement is likely to be done in a range of intermediate scales ($0.5'$ to
20') where neither perturbation theory nor the hierarchical ansatz apply. Here
we explore the behavior of the skewness of $\kappa$ at these intermediate
scales, based on results for the non-linear evolution of the mass bispectrum.
We combined different ray-tracing simulations to test our predictions, and we
find that our calculations describe accurately the transition from the weakly
non-linear to the strongly non-linear regime. We show that the single
lens-plane approximation remains accurate even in the non-linear regime, and we
explicitly calculate the corrections to this approximation. We also discuss the
prospects of measuring the skewness in upcoming weak lensing surveys.
