We present the results of a survey of the analogs of weak Mg ii absorbers ( rest–frame equivalent width W _ { r } ( 2796 ) < 0.3 Å ) at 0 < z < 0.3 . Our sample consisted of 25 HST /STIS echelle quasar spectra ( R = 45 , 000 ) which covered Si ii 1260 and C ii 1335 over this redshift range . Using those similar transitions as tracers of Mg ii facilitates a much larger survey , covering a redshift pathlength of g ( z ) = 5.3 for an equivalent width limit of Mg ii corresponding to W _ { r } ( 2796 ) > 0.02 Å , with 30 \% completeness for the weakest lines . Correcting for incompleteness , we find the number of weak Mg ii absorber analogs with 0.02 < W _ { r } ( 2796 ) < 0.3 Å to be dN / dz = 1.00 \pm 0.20 for 0 < z < 0.3 . This compares to a value of dN / dz = 1.74 \pm 0.10 found by Churchill et al . ( 7 ) for the higher redshift range , 0.4 < z < 1.4 , and is consistent with cosmological evolution of the population . We consider the expected effect on observability of weak Mg ii absorbers of the decreasing intensity of the extragalactic background radiation field from z \sim 1 to z \sim 0 . Assuming that all the objects that produce absorption at z \sim 1 are stable on a cosmological timescale , and that no new objects are created , we would expect dN / dz \sim 2 – 3 at z \sim 0 . About 30 – 50 % of this z \sim 0 population would be decendants of the parsec–scale structures that produce single–cloud , weak Mg ii absorbers at z \sim 1 . The other 50 – 70 % would be lower density , kiloparsec–scale structures that produce C iv absorption , but not detectable low ionization absorption , at z \sim 1 . We conclude that at least one , and perhaps some fraction of both , of these populations has evolved away since z \sim 1 , in order to match the z \sim 0 dN / dz measured in our survey . This would follow naturally for a population of transient structures whose generation is related to star–forming processes , whose rate has decreased since z \sim 1 .