  The quantum mechanical weak value $A_w=\left\langle \phi|A|\psi \right
\rangle / \left\langle \phi | \psi \right\rangle$ of an observable $A$ is a
measurable quantity associated with an observable $A$ and pre- and
post-selected states $\vert\psi \rangle, \vert \phi \rangle$. Much has been
discussed about the meaning and metrological uses of anomalous weak values,
lying outside of the range of eigenvalues of $A$. We present a simple proof
that anomalous weak values require that the (possibly mixed) pre- and post-
selection states have coherence in the eigenbasis of $A$. We also present
conditions under which anomalous $A_w$ are witnesses of generalized
contextuality, dispensing with the operational weak measurement set-up.
