  We study one-loop divergences in Einstein-Maxwell theory and their
implications for the weak gravity conjecture. In particular, we show that
renormalization of these divergences leads to positivity of higher-derivative
corrections to the charge-to-mass ratio of dyonic black holes. This allows
charged extremal black holes to decay into smaller ones, and so the weak
gravity conjecture is automatically satisfied. We also extend this analysis to
a much wider class of Einstein-Maxwell theories coupled to additional massless
matter fields and find the same result. We then go on to study one-loop
divergences in $\mathcal{N} \geq 2$ supergravity and show that dyonic black
holes in these theories are protected against one-loop quantum corrections,
even if the black hole breaks supersymmetry. In particular, extremal dyonic
black holes are stabilized by supersymmetry and cannot decay.
