  Tiny values for gauge couplings of dark photons allow to suppress their kinetic mixing with ordinary photons. We point out that the Weak Gravity Conjecture predicts consequently low ultraviolet cut-offs where new degrees of freedom might appear. In particular, a mixing angle of $\mathcal{O}(10^{-15})$, required in order to fit the excess reported by XENON1T, corresponds to new physics below $\mathcal{O}(100)$ TeV, thus accessible at a Future Circular Collider. We show that possible realizations are provided by compactifications with six large extra dimensions and a string scale of order $\mathcal{O}(100)$ TeV. 
U(1) mixing and the Weak Gravity Conjecture