Machine learning has been widely applied in well logging formation evaluation studies. However, several challenges negatively impacted the generalization capabilities of machine learning models in practical implementations, such as the mismatch of data domain between training and testing datasets, imbalances among sample categories, and inadequate representation of data model. These issues have led to substantial insufficient identification for reservoir and significant deviations in subsequent evaluations. To improve the transferability of machine learning models within limited sample sets, this study proposes a weight transfer learning framework based on the similarity of the labels. The similarity weighting method includes both hard weights and soft weights. By evaluating the similarity between test and training sets of logging data, the similarity results are used to estimate the weights of training samples, thereby optimizing the model learning process. We develop a double experts' network and a bidirectional gated neural network based on hierarchical attention and multi-head attention (BiGRU-MHSA) for well logs reconstruction and lithofacies classification tasks. Oil field data results for the shale strata in the Gulong area of the Songliao Basin of China indicate that the double experts’ network model performs well in curve reconstruction tasks. However, it may not be effective in lithofacies classification tasks, while BiGRU-MHSA performs well in that area. In the study of constructing large-scale well logging processing and formation interpretation models, it is maybe more beneficial by employing different expert models for combined evaluations. In addition, although the improvement is limited, hard or soft weighting methods is better than unweighted (i.e., average-weighted) in significantly different adjacent wells. The code and data are open and available for subsequent studies on other lithofacies layers.