  We compute the corrections from two-photon and photon-Z exchange in
parity-violating elastic electron-proton scattering, used to extract the
strange form factors of the proton. We use a hadronic formalism that
successfully reconciled the earlier discrepancy in the proton's electron to
magnetic form factor ratio, suitably extended to the weak sector. Implementing
realistic electroweak form factors, we find effects of the order 2-3% at Q^2 <
0.1 GeV^2, which are largest at backward angles, and have a strong Q^2
dependence at low Q^2. Two-boson contributions to the weak axial current are
found to be enhanced at low Q^2 and for forward angles. We provide corrections
at kinematics relevant for recent and upcoming parity-violating experiments.
