Uncertainty quantification and negative transfer characterization are significant challenges in the context of deep learning-based remaining useful life prediction with limited data. Conventional Bayesian methods lack scalability to deep learning algorithms for uncertainty quantification due to intricate network connections and extensive training parameters. Additionally, although transfer learning is a promising way to improve the generalization ability of prediction algorithms, its effectiveness is not always guaranteed when leveraging source data undesirably reduces the prediction performance, which is named negative transfer. This manuscript proposed a meta-weighted neural network equipped with uncertainty estimation to discern in-distribution from out-of-distribution data and an adaptive sample meta re-weighting strategy is designed by specifying the weighting function from prediction loss to sample weight according to the gradient direction. Performance evaluations on cryogenic bearings demonstrate that the proposed algorithm can quantitatively determine the weights of source data based on prediction error, ultimately leading to accurate interval remaining life prediction.