This paper investigates a lightweight deep reinforcement learning (DRL)-assisted weighting framework for CSI-free multi-satellite positioning in LEO constellations, where each visible satellite provides one serving beam (one pilot response) per epoch. A discrete-action Deep Q-Network (DQN) learns satellite weights directly from received pilot measurements and geometric features, while an augmented weighted least squares (WLS) estimator provides physics-consistent localization and jointly estimates the receiver clock bias. The proposed hybrid design targets an accuracy-runtime trade-off rather than absolute supervised optimality. In a representative 2-D setting with 10 visible satellites, the proposed approach achieves sub-meter accuracy (0.395m RMSE) with low computational overhead, supporting practical deployment for resource-constrained LEO payloads.