This letter investigates the weighted sum rate maximization problem in movable antenna (MA)-enhanced systems. To reduce the computational complexity, we transform it into a more tractable weighted minimum mean square error (WMMSE) problem well-suited for MA. We then adopt the WMMSE algorithm and majorization-minimization algorithm to optimize the beamforming and antenna positions, respectively. Moreover, we propose a planar movement mode, which constrains each MA to a specified area, we obtain a low-complexity closed-form solution. Numerical results demonstrate that the MA-enhanced system outperforms the conventional system. Besides, the computation time for the planar movement mode is reduced by approximately 30\% at a little performance expense.