Four Ophiuchus binaries, two Class I systems and two Class II systems, with separations of ~450-1100 AU, were observed with the Owens Valley Radio Observatory (OVRO) millimeter interferometer. In each system, the 3 mm continuum maps show dust emission at the location of the primary star, but no emission at the position of the secondary. This result is different from observations of less evolved Class 0 binaries, in which dust emission is detected from both sources. The nondetection of secondary disks is, however, similar to the dust distribution seen in wide Class II Taurus binaries. The combined OVRO results from the Ophiuchus and Taurus binaries suggest that secondary disk masses are significantly lower than primary disk masses by the Class II stage, with initial evidence that massive secondary disks are reduced by the Class I stage. Although some of the secondaries retain hot inner disk material, the early dissipation of massive outer disks may negatively impact planet formation around secondary stars. Masses for the circumprimary disks are within the range of masses measured for disks around single T Tauri stars and, in some cases, larger than the minimum mass solar nebula. More massive primary disks are predicted by several formation models and are broadly consistent with the observations. Combining the 3 mm data with previous 1.3 mm observations, the dust opacity power-law index for each primary disk is estimated. The opacity index values are all less than the scaling for interstellar dust, possibly indicating grain growth within the circumprimary disks.