A system consisting of two point charges has an energy contribution from the system electrostatic potential energy and accordingly a contribution to the system mass given by this energy divided byc2. Here we investigate the change in weight associated with the electrostatic potential energy for a system of two point charges supported side by side against a weak gravitational field. The gravitational distortion of the Coulomb field of a point charge is calculated using the equivalence principle, and it is then shown that the change in the two‐particle system weight can be understood precisely as the change in supporting force necessary to balance the electric force of each charge upon the other. The example provides a clear illustration and detailed mechanism for understanding the mass‐energy connection for weak gravitational fields.