Recent work has shown that UV-luminous reionization-era galaxies often exhibit strong Lyman-alpha emission despite being situated at redshifts where the IGM is thought to be substantially neutral. It has been argued that this enhanced Ly alpha transmission reflects the presence of massive galaxies in overdense regions which power large ionized bubbles. An alternative explanation is that massive galaxies shift more of their Ly alpha profile to large velocities (relative to the systemic redshift) where the IGM damping wing absorption is reduced. Such a mass-dependent trend is seen at lower redshifts, but whether one exists at z similar to 7 remains unclear owing to the small number of existing systemic redshift measurements in the reionization era. This is now changing with the emergence of [C ii]-based redshifts from ALMA. Here, we report MMT/Binospec Ly alpha spectroscopy of eight UV-bright (M-UV similar to -22) galaxies at z similar or equal to 7 selected from the ALMA REBELS survey. We detect Ly alpha in four of eight galaxies and use the [C ii] systemic redshifts to investigate the Ly alpha velocity profiles. The Ly alpha lines are significantly redshifted from systemic (average velocity offset = 223 km s(-1)) and broad (FWHM approximate to 300-650 km s(-1)), with two sources showing emission extending to approximate to 750 km s(-1). We find that the broadest Ly alpha profiles are associated with the largest [C ii] line widths, suggesting a potential link between the Ly alpha FWHM and the dynamical mass. Since Ly alpha photons at high velocities transmit efficiently through the z = 7 IGM, our data suggest that velocity profiles play a significant role in boosting the Ly alpha visibility of the most UV-luminous reionization-era galaxies.