  We experimentally determine weak values for a single photon's polarization,
obtained via a weak measurement that employs a two-photon entangling operation,
and postselection. The weak values cannot be explained by a semiclassical wave
theory, due to the two-photon entanglement. We observe the variation in size of
the weak value with measurement strength, obtaining an average measurement of
the S_1 Stokes parameter more than an order of magnitude outside of the
operator's spectrum for the smallest measurement strengths.
