In dynamic wireless environments, accurate channel state information (CSI) prediction remains challenging due to non-stationary fading, mobility. This paper proposes an Uncertainty-Weighted Experience Replay (UW-ER) framework that integrates model uncertainty into the replay sampling process to improve robustness in online CSI prediction. A lightweight LSTM architecture with Monte-Carlo dropout is employed to estimate predictive variance, which is then used to adaptively weight the reconstruction loss for each training sample. The proposed method is evaluated on a UMi-Dense MIMO channel dataset generated using a stochastic fading model consistent with 3GPP standards. Results show that UW-ER achieves stable generalization, with validation NMSE centered near 0 dB and a strong correlation (r = 0.93) between predicted uncertainty and reconstruction error, indicating well-calibrated confidence estimates. Ablation studies demonstrate that the LARS-based replay policy achieves competitive performance with smaller memory budgets compared to conventional reservoir replay. Overall, the UW-ER approach improves continual channel learning stability without increasing computational complexity, offering a scalable solution for future 6G adaptive communication systems.