A STAR-RIS assisted two-user full-duplex communication system is studied in which the multiantenna base station (BS) and single-antenna users are subject to maximum transmission power constraints. Firstly, for three well known protocols of STAR-RIS, weighted sum rate (WSR) is derived as the main performance metric. Next, the corresponding resource allocation problems are reformulated and converted into some equivalent weighted minimum mean-square-error forms and then transformed into several convex sub-problems. It is shown that this conversion allows us to solve the problems iteratively and efficiently. Although the original WSR optimization is non convex, the proposed efficient iterative alternating procedure is shown to achieve an acceptable sub-optimal performance. For the considered setup, the STAR-RIS’s tunable parameters are optimized via the successive convex approximation technique. Finally, the performance of the proposed schemes is compared against some baselines and shown to be superior to the conventional RIS.