  Heisenberg-limited and weak measurements are the two intriguing notions, used
in recent times for enhancing the sensitivity of measurements in quantum
metrology. Using a quantum cat state, endowed with sub-Planck structure, we
connect these two novel concepts. It is demonstrated that these two phenomena
manifest in complementary regimes, depending upon the degree of overlap between
the mesoscopic states constituting the cat state under consideration. In
particular, we find that when sub-Planck structure manifests, the imaginary
weak value is obscured and vice-versa.
