Enhancing user fairness in advanced multi-user systems like two-layer rate-splitting multiple access (RSMA) is a critical yet challenging task. This letter proposes a novel movable antenna (MA) approach to address this challenge. We formulate a max-min fairness problem, maximizing the minimum user rate, a key metric for fairness, through the joint optimization of the beamforming matrices, user clustering, common rate allocation, and the antenna position vector (APV). To solve this non-convex problem, we develop an efficient two-loop iterative algorithm. The outer-loop leverages the dynamic neighborhood pruning particle swarm optimization method to find a high-quality APV, while the inner-loop optimizes the remaining variables for a given APV. Simulation results validate our approach, demonstrating that the proposed scheme yields significant fairness gains over various benchmark schemes.