A covariant classical theory of gravity is given assuming absolute flat spacetime and the strong equivalence principle (SEP). It is shown that adherence to these postulates requires that the gravitational field “dimensionally perturb” all physical objects at a location universally. Such perturbations are referred to as “gravity shifts,” and it is found that all gravitational phenomena may be given in terms of them. Two classes of observers emerge in “gravity shift theory”—“natural observers” using gravity shifted instruments as is, applicable for all presently available observations, and “absolute observers” that correct for the gravity shifting applied to instruments. Absolute observers accurately measure quantities, including the absolute spacetime metric as it actually is. Natural observers do not accurately measure quantities, but their system of measurement is observationally consistent, yielding a curved “natural metric” to characterize spacetime. When a local gravitational system is surrounded by a “background system” with negligible curvature effects, its gravity shifting induces a diffeomorphism applied to the local system, yielding satisfaction of the SEP for natural observers. Using the naturally observed inertial form of physical law in free-fall frames, covariant formulation in all coordinates establishes the natural metric as the universally coupled “gravitational metric” in physical law. The unique field equation determining gravity shifts, and therefore the natural metric, is developed. The resultant bimetric theory is parameterless, complete, and self-consistent. The field equation yields the observed post-Newtonian natural metric and linearizes to the predictive linearized Einstein equation, which, along with SEP satisfaction, results in successful prediction of a wide variety of observed gravitational phenomena. A supplement is provided that extends the range of predictions to include low post-Newtonian order radiation cases, and also the strong-field cases consisting of the properties of black and neutron stars plus any nearby matter and light, where in all cases, the predictions are shown to be consistent with observations.