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Ensuring user fairness in wireless communications is a fundamental challenge, as balancing the trade-off between fairness and sum rate leads to a non-convex, multi-objective optimization whose complexity grows with network scale. To alleviate this conflict, we propose an optimization-based unsupervised learning approach based on the wireless transformer (WiT) architecture that learns from channel state information (CSI) features. We reformulate the trade-off by combining the sum rate and fairness objectives through a Lagrangian multiplier, which is updated automatically via a dual-ascent algorithm. This mechanism allows for a controllable fairness constraint while simultaneously maximizing the sum rate, effectively realizing a trace on the Pareto front between two conflicting objectives. Our findings show that the proposed approach offers a flexible solution for managing the trade-off optimization under prescribed fairness.