  We study the sensitivity of weak lensing by large scale structures to the
evolution of dark energy. We explore a 2-parameters model of dark energy
evolution, inspired by tracking quintessence models. To this end, we compute
the likelihood of a few representative models with varying and non varying
equation of states. Based on an earlier work, we show that the evolution of
dark energy has a much stronger impact on the non-linear structure growth than
on the angular diameter distance, which makes large scale structure
measurements a very efficient probe of this evolution. For the different
models, we investigate the dark energy parameters degeneracies with the mass
power spectrum shape Gamma, normalisation sigma_8, and with the matter mean
density Omega_M. This result is a strong motivation for performing large scale
structure simulations beyond the simple constant dark energy models, in order
to calibrate the non-linear regime accurately. Prospective for the Canada
France Hawaii Telescope Legacy Survey (CFHTLS) and Super-Novae Acceleration
Probe (SNAP) are given. These results complement nicely the cosmic microwave
background and Super-Novae constraints. Weak lensing is shown to be more
sensitive to a variation of the equation of state, whereas CMB and SNIa give
information on its constant part.
