Due to electron-nucleus weak interaction, atomic bound states with different parities turn out to be mixed. We discuss a prospective method for measuring the mixing parameter between the nearly degenerate metastable states 1s 1/2 2s 1/2 : J = 0 and 1s 1/2 2p 1/2 : J = 0 in heliumlike uranium. Our analysis is based on the polarization properties of the photons emitted in the two-photon decays of such states.