High resolution optical (HIRES/Keck) and UV (STIS/HST) spectra, covering a large range of chemical transitions, are analyzed for three single-cloud weak MgII absorption systems along the line of sight toward the quasar PG 1634+706. Weak MgII absorption lines in quasar spectra trace metal-enriched environments that are rarely closely associated with the most luminous galaxies (>0.05L^*). The two weak MgII systems at z=0.81 and z=0.90 are constrained to have >=solar metallicity, while the metallicity of the z=0.65 system is not as well-constrained, but is consistent with >1/10th solar. These weak MgII clouds are likely to be local pockets of high metallicity in a lower metallicity environment. All three systems have two phases of gas, a higher density region that produces narrower absorption lines for low ionization transitions, such as MgII, and a lower density region that produces broader absorption lines for high ionization transitions, such as CIV. The CIV profile for one system (at z=0.81) can be fit with a single broad component (b~10 km/s), but those for the other two systems require one or two additional offset high ionization clouds. Two possible physical pictures for the phase structure are discussed: one with a low-ionization, denser phase embedded in a lower density surrounding medium, and the other with the denser clumps surrounding more highly ionized gas.