We investigate the phenomenology of a heavy scalar ϕ of the type involved in Bekenstein's framework for varying electromagnetic coupling theories, with the difference that the scalar in our model has a large mass. The model has only two free parameters, the mass Mϕ of the scalar and the scale Λ of new physics. The scalar is dominantly produced through photon–photon fusion at the LHC and leads to a diphoton final state. It can also be produced by quark–antiquark fusion in association with a photon or a fermion pair. Its dominating decay is to diphotons, but it also has a large three-body branching to a fermion pair and a photon, which can provide an interesting search channel with a dilepton–photon resonance. We derive exclusion limits on the Mϕ−Λ plane from the latest 13 TeV LHC diphoton resonance search data. For a benchmark mass of Mϕ∼1 TeV, we find a lower limit on Λ of 18 TeV. We discuss the more complex possibility of varying couplings in the full electroweak theory and comment on the possibility that the new physics is related to extra dimensions or string theory.