  Parity-violating elastic electron-nucleon scattering at low momentum transfer
allows one to access the nucleon's weak charge, the vector coupling of the
$Z$-boson to the nucleon. In the Standard Model and at tree level, the weak
charge of the proton is related to the weak mixing angle and accidentally
suppressed, $Q_W^{p,\,{\rm tree}}=1-4\sin^2\theta_W\approx0.07$. Modern
experiments aim at extracting $Q_W^p$ at $\sim1\%$ accuracy. Similarly, parity
non-conservation in atoms allows to access the weak charge of atomic nuclei. We
consider a novel class of radiative corrections, an exchange of two photons
with parity violation in the hadronic/nuclear system. These corrections may
affect the extraction of $\sin^2\theta_W$ from the experimental data at the
relevant level of precision because they are affected by long-range
interactions similar to other parity-violating radiative corrections, such as,
e.g., the $\gamma Z$-exchange, which has obtained much attention recently. We
show that the significance of this new correction increases with the beam
energy in parity-violating electron scattering, but the general properties of
the parity-violating forward Compton amplitude protect the formal definition of
the weak charge as a limit at zero-momentum transfer and zero-energy. We also
discuss the relevance of the new correction for upcoming experiments.
