Recent cosmological observations and compatible theory offer an understanding of long-mysterious dark matter and dark energy. The postulate of universal conformal local Weyl scaling symmetry, without dark matter, modifies action integrals for both Einstein–Hilbert gravitation and the Higgs scalar field by gravitational terms. Conformal theory accounts for both observed excessive external galactic orbital velocities and for accelerating cosmic expansion. SU(2) symmetry-breaking is retained by the conformal scalar field, which does not produce a massive Higgs boson, requiring an alternative explanation of the observed LHC 125 GeV resonance. Conformal theory is shown here to be compatible with a massive neutral particle or resonance W2W2 at 125 GeV, described as binary scalars gμνWμ−Wν+gμνWμ−Wν+ and gμνZμ∗ZνgμνZμ∗Zν interacting strongly via quark exchange. Decay modes would be consistent with those observed at LHC. Massless scalar field ΦΦ is dressed by the W2W2 field to produce Higgs Lagrangian term λ(Φ†Φ)2λ(Φ†Φ)2 with the empirical value of λλ known from astrophysics.