We report the discovery of two iron–group enhanced high–metallicity Mg ii absorbers in a search through 28 Ly \alpha forest clouds along the PKS 0454+039 sight line . Based upon our survey and the measured redshift number densities of W _ { r } ( { \hbox { { Mg } \kern 1.0 pt { \sc ii } } } ) \leq 0.3 Å absorbers and Ly \alpha absorbers at z \sim 1 , we suggest that roughly 5 % of Ly \alpha absorbers at z \leq 1 will exhibit “ weak ” Mg ii absorption to a 5 \sigma W _ { r } ( \lambda 2796 ) detection limit of 0.02 Å . The two discovered absorbers , at redshifts z = 0.6248 and z = 0.9315 , have W _ { r } ( { \hbox { { Ly } \kern 1.0 pt$ \alpha$ } } ) = 0.33 and 0.15 Å , respectively . Based upon photoionization modeling , the H i column densities are inferred to be in the range 15.8 \leq \log N ( { \hbox { { H } \kern 1.0 pt { \sc i } } } ) \leq 16.8 cm ^ { -2 } . For the z = 0.6428 absorber , if the abundance pattern is solar , then the cloud has [ \hbox { Fe / H } ] > -1 ; if its gas–phase abundance follows that of depleted clouds in our Galaxy , then [ \hbox { Fe / H } ] > 0 is inferred . For the z = 0.9315 absorber , the metallicity is [ \hbox { Fe / H } ] > 0 , whether the abundance pattern is solar or suffers depletion . Imaging and spectroscopic studies of the PKS 0454+039 field reveal no candidate luminous objects at these redshifts . We discuss the possibility that these Mg ii absorbers may arise in the class of “ giant ” low surface brightness galaxies , which have [ \hbox { Fe / H } ] \geq - 1 , and even [ \hbox { Fe / H } ] \geq 0 , in their extended disks . We tentatively suggest that a substantial fraction of these “ weak ” Mg ii absorbers may select low surface brightness galaxies out to z \sim 1 .