We examine possible environmental sources of the enhanced star formation and active galactic nucleus (AGN) activity in the z=3.09 SSA22 protocluster using Hubble WFC3 F160W (~1.6{mu}m) observations of the SSA22 field, including new observations centered on eight X-ray selected protocluster AGN. To investigate the role of mergers in the observed AGN and star formation enhancement, we apply both quantitative (Sersic-fit and Gini-M20) and visual morphological classifications to F160W images of protocluster Lyman-break galaxies (LBGs) in the fields of the X-ray AGN and z~3 field LBGs in SSA22 and GOODS-N. We find no statistically significant differences between the morphologies and merger fractions of protocluster and field LBGs, though we are limited by small number statistics in the protocluster. We also fit the UV-to-near-IR spectral energy distributions of F160W-detected protocluster and field LBGs to characterize their stellar masses and star formation histories. We find that the mean protocluster LBG is a factor of ~2 times more massive and more attenuated than the mean z~3 field LBG. We take our results to suggest that ongoing mergers are not more common among protocluster LBGs than field LBGs, though protocluster LBGs appear to be more massive. We speculate that the larger mass of the protocluster LBGs contributes to the enhancement of SMBH mass and accretion rate in the protocluster, which in turn drives the observed protocluster AGN enhancement.