We study the Lyα profiles of 36 spectroscopically detected Lyα-emitters (LAEs) at z ∼ 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 R = 26.0, and ranges from R 23 to R > 27, corresponding to rest-frame UV absolute magnitudes M UV −22 to M UV > −18.2. Dynamical masses range from M dyn < 1.3 × 10 8 M to M dyn = 6.8 × 10 9 M , with a median value of M dyn = 6.3 × 10 8 M . Thirty of the 36 Lyα emission lines are redshifted with respect to the systemic velocity with at least 1σ significance, and the velocity offset with respect to systemic Δv Lyα is correlated with the R-band magnitude, M UV , and the velocity dispersion measured from nebular emission lines with >3σ significance: brighter galaxies with larger velocity dispersions tend to have larger values of Δv Lyα . We also make use of a comparison sample of 122 UV-color-selected R < 25.5 galaxies at z ∼ 2, all with Lyα 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 Δv Lyα is anti-correlated with the Lyα equivalent width with 7σ significance. Our results are consistent with a scenario in which the Lyα profile is determined primarily by the properties of the gas near the systemic redshift; in such a scenario, the opacity to Lyα 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.