The fluid antenna system (FAS) is a disruptive tech-nology for future wireless communication networks. This paper considers the joint optimization of beamforming matrices and antenna positions for weighted sum rate (WSR) maximization in fluid antenna (FA)-assisted multiuser multiple-input multiple-output (MU-MIMO) networks, which presents significant chal-lenges due to the strong coupling between beamforming and FA positions, the non-concavity of the WSR objective function, and high computational complexity. To address these challenges, we first propose a novel block coordinate ascent (BCA)-based method that employs matrix fractional programming techniques to reformulate the original complex problem into a more tractable form. Then, we develop a parallel majorization maximization (MM) algorithm capable of optimizing all FA positions simul-taneously. To further reduce computational costs, we propose a decentralized implementation based on the decentralized base-band processing (DBP) architecture. Simulation results demon-strate that our proposed algorithm not only achieves significant WSR improvements over conventional MIMO networks but also outperforms the existing method. Moreover, the decentralized implementation substantially reduces computation time while maintaining similar performance compared with the centralized implementation.