We study the Ly \alpha profiles of 36 spectroscopically-detected Ly \alpha -emitters ( LAEs ) at z \sim 2 –3 , using Keck MOSFIRE to measure systemic redshifts and velocity dispersions from rest-frame optical nebular emission lines . The sample has a median optical magnitude { \cal R } = 26.0 , and ranges from { \cal R } \simeq 23 to { \cal R } > 27 , corresponding to rest-frame UV absolute magnitudes M _ { UV } \simeq - 22 to M _ { UV } > -18.2 . Dynamical masses range from M _ { dyn } < 1.3 \times 10 ^ { 8 } M _ { \odot } to M _ { dyn } = 6.8 \times 10 ^ { 9 } M _ { \odot } , with a median value of M _ { dyn } = 6.3 \times 10 ^ { 8 } M _ { \odot } . Thirty of the 36 Ly \alpha emission lines are redshifted with respect to the systemic velocity with at least 1 \sigma significance , and the velocity offset with respect to systemic \Delta v _ { Ly \alpha } is correlated with { \cal R } -band magnitude , M _ { UV } , and the velocity dispersion measured from nebular emission lines with > 3 \sigma significance : brighter galaxies with larger velocity dispersions tend to have larger values of \Delta v _ { Ly \alpha } . We also make use of a comparison sample of 122 UV-color-selected { \cal R } < 25.5 galaxies at z \sim 2 , all with Ly \alpha emission and systemic redshifts measured from nebular emission lines . Using the combined LAE and comparison samples for a total of 158 individual galaxies , we find that \Delta v _ { Ly \alpha } is anti-correlated with the Ly \alpha equivalent width with 7 \sigma significance . 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 .