The complete gauge-invariant set of the one-loop QED corrections to the parity-nonconserving 6s-7s amplitude in Cs133 is evaluated to all orders in αZ using a local version of the Dirac-Hartree-Fock potential. The calculations are performed in both length and velocity gauges for the absorbed photon. The total binding QED correction is found to be -0.27(3)%. The weak charge of Cs133, derived using two most accurate values of the vector transition polarizability β, is QW=-72.57(46) for β=26.957(51)aB3 and QW=-73.09(54) for β=27.15(11)aB3. The first value deviates by 1.1σ from the prediction of the standard model, while the second one is in perfect agreement with it.