  We explore the sensitivity of weak gravitational lensing to second-order
corrections to the spacetime metric within a cosmological adaptation of the
parameterized post-Newtonian framework. Whereas one might expect nonlinearities
of the gravitational field to introduce non-Gaussianity into the statistics of
the lensing convergence field, we show that such corrections are actually
always small within a broad class of scalar-tensor theories of gravity. We show
this by first computing the weak lensing convergence within our parameterized
framework to second order in the gravitational potential, and then computing
the relevant post-Newtonian parameters for scalar-tensor gravity theories. In
doing so we show that this potential systematic factor is generically
negligible, thus clearing the way for weak lensing to provide a direct tracer
of mass on cosmological scales for a wide class of gravity theories despite
uncertainties in the precise nature of the departures from general relativity.
