Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric formulation to assign eigenvalues to unmeasured observables of a system, which results in logical paradoxes, and no clear physical picture. A top-down ontological model is introduced that treats the weak values of observables as physically real during the time between pre- and post-selection (PPS), which avoids these paradoxes. The generally delocalized rank-1 projectors of a quantum system describe its fundamental ontological elements, and the highest-rank projectors corresponding to individual localized objects describe an emergent particle model, with unusual particles, whose masses and energies may be negative or imaginary. This retrocausal top-down model leads to an intuitive particle-based ontological picture, wherein weak measurements directly probe the properties of these exotic particles, which exist whether or not they are actually measured.
Keywords: quantum measurement; quantum paradoxes; quantum physics; time-symmetry; weak values.