This letter investigates the weighted sum rate maximization problem in movable antenna (MA)-enhanced systems, aiming to reduce computational complexity. The problem is transformed into a weighted minimum mean square error (WMMSE) problem, and the WMMSE algorithm and majorization-minimization (MM) algorithm are used to optimize the beamforming and antenna positions, respectively. A planar movement mode is proposed, where each MA is constrained to a specified area, to achieve a low-complexity closed-form solution. Numerical results show that the MA-enhanced system outperforms conventional systems, and the planar movement mode reduces computation time by about 30% with minimal performance loss. The proposed algorithm is convergent and efficient, demonstrating the potential of MAs in enhancing wireless communication systems.This letter investigates the weighted sum rate maximization problem in movable antenna (MA)-enhanced systems, aiming to reduce computational complexity. The problem is transformed into a weighted minimum mean square error (WMMSE) problem, and the WMMSE algorithm and majorization-minimization (MM) algorithm are used to optimize the beamforming and antenna positions, respectively. A planar movement mode is proposed, where each MA is constrained to a specified area, to achieve a low-complexity closed-form solution. Numerical results show that the MA-enhanced system outperforms conventional systems, and the planar movement mode reduces computation time by about 30% with minimal performance loss. The proposed algorithm is convergent and efficient, demonstrating the potential of MAs in enhancing wireless communication systems.