  It is argued that a weak value of an observable is a robust property of a
single pre- and post-selected quantum system rather than a statistical
property. During an infinitesimal time a system with a given weak value affects
other systems as if it were in an eigenstate with eigenvalue equal to the weak
value. This differs significantly from the action of a system pre-selected only
and possessing a numerically equal expectation value. The weak value has a
physical meaning beyond a conditional average of a pointer in the weak
measurement procedure. The difference between the weak value and the
expectation value has been demonstrated on the example of photon polarization.
In addition, the weak values for systems pre- and post-selected in mixed states
are considered.
