We present a set of predictions for weak lensing correlation functions in the context of modified gravity models, including a prescription for the impact of the non-linear power spectrum regime in these models. We consider the Dvali, Gabadadze & Porrati and f(R) models, together with dark energy models with the same expansion history. We use the requirement that gravity is close to general relativity on small scales to estimate the non-linear power for these models. We then calculate weak lensing statistics, showing their behaviour as a function of scale and redshift, and present predictions for measurement accuracy with future lensing surveys, taking into account cosmic variance and galaxy shape noise. We demonstrate the improved discriminatory power of weak lensing for testing modified gravities once the non-linear power spectrum contribution has been included. We also examine the ability of future lensing surveys to constrain a parametrization of the non-linear power spectrum, including sensitivity to the growth factor.