  We study the effect of modifications to General Relativity on large scale
weak lensing observables. In particular, we consider three modified gravity
scenarios: f(R) gravity, the DGP model, and TeVeS theory. Weak lensing is
sensitive to the growth of structure and the relation between matter and
gravitational potentials, both of which will in general be affected by modified
gravity. Restricting ourselves to linear scales, we compare the predictions for
galaxy-shear and shear-shear correlations of each modified gravity cosmology to
those of an effective Dark Energy cosmology with the same expansion history. In
this way, the effects of modified gravity on the growth of perturbations are
separated from the expansion history. We also propose a test which isolates the
matter-potential relation from the growth factor and matter power spectrum. For
all three modified gravity models, the predictions for galaxy and shear
correlations will be discernible from those of Dark Energy with very high
significance in future weak lensing surveys. Furthermore, each model predicts a
measurably distinct scale dependence and redshift evolution of galaxy and shear
correlations, which can be traced back to the physical foundations of each
model. We show that the signal-to-noise for detecting signatures of modified
gravity is much higher for weak lensing observables as compared to the ISW
effect, measured via the galaxy-CMB cross-correlation.
