The Wilson-Bappu effect (WBE) is a remarkable correlation between the width of the chromospheric emission core of the CaII 3934{AA} K line and stellar absolute visual magnitude over an astonishing range, from diminutive red dwarfs to bloated yellow supergiants. The WBE signifies a deep connection between the nonclassical, mechanically heated chromosphere and fundamental stellar properties. The present study considers the parallel WBE in the analogous MgII k line at 2796{AA}, utilizing near-ultraviolet spectra from Hubble Space Telescope (HST), and stellar parameters mainly derived from Gaia. The final sample is 300 stars (301 including the Sun). The high cosmic abundance of magnesium allowed MgII k emissions to be recovered in the warmer F-types, at the edge of convection and chromospheric activity, and in low-activity Sunlike dwarfs-situations in which CaII K might be too weak to measure. Nevertheless, the derived slope of the MgII WBE was similar to previous reports based on the K line; as well as other MgII efforts with smaller samples of pre-HST spectra. Further, a decomposition of the MgII WBE in temperature, gravity, activity, and metallicity yielded similar results to previous CaII work, but with the greater clarity afforded by the large, diverse HST sample. Parametric dependences of the k-line WBE match, tolerably well, predictions based on the "ionization-valve" theory of chromospheric structure. In the end, the WBE is not merely an astrophysical curiosity, but rather informs the question of how chromospheres-arguably the central bastion of nonclassical heating-have come to be.