  We study the Lya profiles of 36 spectroscopically-detected Lya-emitters
(LAEs) at z2-3, 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 R23 to R>27, corresponding to
rest-frame UV absolute magnitudes M_UV-22 to M_UV>-18.2. Dynamical masses range
from M_dyn<1.3e8 Msun to M_dyn=6.8e9 Msun, with a median value of M_dyn=6.3e8
Msun. Thirty of the 36 Lya emission lines are redshifted with respect to the
systemic velocity with at least 1 sigma significance, and the velocity offset
with respect to systemic dv_Lya is correlated with 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 dv_Lya. We also make use of a comparison sample of 122
UV-color-selected R<25.5 galaxies at z2, all with Lya 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 dv_Lya
is anti-correlated with the Lya equivalent width with 7 sigma significance. Our
results are consistent with a scenario in which the Lya profile is determined
primarily by the properties of the gas near the systemic redshift; in such a
scenario, the opacity to Lya 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.
