  Taking a thermodynamic perspective, we study the weak gravity conjecture in
the context of 4D Einstein-Maxwell-dilaton theory. We find closed-form
expressions for the corrected thermodynamic quantities in the presence of
four-derivative terms in the action, and in particular the charge-to-mass ratio
and entropy, for several families of solutions of special magnetic-to-electric
charge ratio or dilaton coupling constant. Assuming that dyonic black holes
themselves are the conjectured charged states, this places constraints on the
Wilson coefficients of the theory which we show are satisfied under mild
assumptions on the UV theory.
