Single-stage fine-tuning is pervasive, yet catastrophic forgetting persists when the source pre-training data is inaccessible. Data weighting affords a natural lever to modulate sample influence. Yet existing weighting methods lack a principled mechanism to explicitly arbitrate knowledge retention against new-task adaptation, and provide no unified differentiable objective to accommodate auxiliary signals such as sample diversity and sample characteristics. This is because current schemes privilege one goal over the other, and no explicit gradient-compatible encoding exists for such signals. To address this, we propose DRIVE, a principled and efficient weight assignment framework. It derives per-sample weights via a unified differentiable objective where three coupled signals co-evolve: Shapley additivity splits contribution into anti-forgetting and adaptation components, which are reshaped by a covariance-based diversity term and stabilized by a sample-characteristic prior. Far from a mere combination, this yields an end-to-end gradient-based scheme balancing stability against plasticity. Theoretically, we prove that DRIVE enjoys superior stability-plasticity guarantees over existing weighting schemes and enhances parameter estimation robustness. Empirically, it attains superior overall performance, faster convergence, and stronger robustness. Code at https://github.com/luciabcd/DRIVE.

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