A new heavy resonance may be observable at the LHC if it has a significant decay branching fraction into a pair of photons. We entertain this possibility by looking at the modest excess in the diphoton invariant mass spectrum around 750 GeV recently reported in the ATLAS and CMS experiments. Assuming that it is a spinless boson, dubbed s˜, we consider it within a model containing two weak scalar doublets having zero vacuum expectation values and a scalar singlet in addition to the doublet responsible for breaking the electroweak symmetry. The model also possesses three Dirac neutral singlet fermions, the lightest one of which can play the role of dark matter and which participate with the new doublet scalars in generating light neutrino masses radiatively. We show that the model is consistent with all phenomenological constraints and can yield a production cross section σ(pp→s˜→γγ) of roughly the desired size, mainly via the photon-fusion contribution, without involving extra colored fermions or bosons. We also discuss other major decay modes of s˜ which are potentially testable in upcoming LHC measurements.