  Surveys of weak gravitational lensing of distant galaxies will be one of the
key cosmological probes in the future. We study the ability of such surveys to
constrain neutrino masses and the equation of state parameter of the dark
energy, focussing on how tomographic information can improve the sensitivity to
these parameters. We also provide a detailed discussion of systematic effects
pertinent to weak lensing surveys, and the possible degradation of sensitivity
to cosmological parameters due to these effects. For future probes such as the
Large Synoptic Survey Telescope survey, we find that, when combined with cosmic
microwave background data from the Planck satellite, a sensitivity to neutrino
masses of sigma(sum m_nu) < 0.05 eV can be reached. This results is robust
against variations in the running of the scalar spectral index, the
time-dependence of dark energy equation of state, and/or the number of
relativistic degrees of freedom.
