  We connect the weak measurements framework to the path integral formulation
of quantum mechanics. We show how Feynman propagators can in principle be
experimentally inferred from weak value measurements. We also obtain
expressions for weak values parsing unambiguously the quantum and the classical
aspects of weak couplings between a system and a probe. These expressions are
shown to be useful in quantum chaos related studies (an illustration involving
quantum scars is given), and also in solving current weak-value related
controversies (we discuss the existence of discontinuous trajectories in
interferometers and the issue of anomalous weak values in the classical limit).
