  We explore possible extensions of the Weak Gravity Conjecture (WGC) to scalar
field theories. To avoid charged black hole remnants, the WGC requires the
existence of a particle with a mass $m < g q M_P$, with charge $q$ and U(1)
gauge coupling $g$, allowing the decay to shed the black hole charge. Although
there is no obvious problem that arises in the absence of a U(1) charge, it has
been postulated that gravity must remain the weakest force even when extended
to scalar interactions. Quantifying this conjecture may be done by comparing
scalar and gravitational amplitudes, or as we advocate here by comparing
scattering cross sections. In theories with non-trivial field space geometries,
by working out examples with perturbation theory around arbitrary field values
and performing tadpole resummations, we argue that the conjecture must be
applied only at the extrema of the scalar potential (when expressed in locally
canonical coordinates). We consider several toy models in the context of
no-scale supergravity and also consider examples of inflationary models.
