We study the Ly alpha profiles of 36 spectroscopically detected Ly alpha -emitters (LAEs) at z ~ 2-3, using Keck MOSFIRE to measure systemic redshifts and velocity dispersions from rest-frame optical nebular emission lines. Thirty of the 36 Ly alpha emission lines are redshifted with respect to the systemic velocity with at least lsigma significance, and the velocity offset with respect to systemic Delta v sub(Ly) alpha is correlated with the R-band magnitude, M sub(UV), and the velocity dispersion measured from nebular emission lines with >3sigma significance: brighter galaxies with larger velocity dispersions tend to have larger values of Delta v sub(Ly) alpha . Our results are consistent with a scenario in which the Ly alpha profile is determined primarily by the properties of the gas near the systemic redshift; in such a scenario, the opacity to Ly alpha photons in lower mass galaxies may be reduced if large gaseous disks have not yet developed and if the gas is ionized by the harder spectrum of young, low metallicity stars.