  When the weak value of a projector is 1, a quantum system behaves as in that
eigenstate with probability 1. By definition, however, the weak value may take
an anomalous value lying outside the range of probability like -1. From the
viewpoint of a physical effect, we show that such a negative weak value of -1
can be regarded as the counterpart of the ordinary value of 1. Using photons,
we experimentally verify it as the symmetrical shift in polarization depending
on the weak value given by pre-postselection of the path state. Unlike
observation of a weak value as an ensemble average via weak measurements, the
effect of a weak value is definitely confirmed in two photon interference: the
symmetrical shift corresponding to the weak value can be directly observed as
the rotation angle of a half wave plate.
