  We generalize tensor-scalar theories of gravitation by the introduction of an
abnormally weighting type of energy. This theory of tensor-scalar anomalous
gravity is based on a relaxation of the weak equivalence principle that is now
restricted to ordinary visible matter only. As a consequence, the convergence
mechanism toward general relativity is modified and produces naturally cosmic
acceleration as an inescapable gravitational feedback induced by the
mass-variation of some invisible sector. The cosmological implications of this
new theoretical framework are studied. This glimpses at an enticing new
symmetry between the visible and invisible sectors, namely that the scalar
charges of visible and invisible matter are exactly opposite.
