We examine the interference γZ box corrections to parity-violating elastic electron–proton scattering in the light of the recent observation of quark–hadron duality in parity-violating deep-inelastic scattering from the deuteron, and the approximate isospin independence of duality in the electromagnetic nucleon structure functions down to Q2≈1 GeV2. Assuming that a similar behavior also holds for the γZ proton structure functions, we find that duality constrains the γZ box correction to the proton's weak charge to be ℜe□γZV=(5.4±0.4)×10−3 at the kinematics of the Qweak experiment. Within the same model we also provide estimates of the γZ corrections for future parity-violating experiments, such as MOLLER at Jefferson Lab and MESA at Mainz.