Randomized neural networks have gained attention for their ability to overcome the limitations of traditional models, offering efficiency in tasks such as classification and regression. Among these, the Random Vector Functional Link Network (RVFL) and its enhanced versions, including the Ensemble Deep RVFL (edRVFL) and Weighting and Pruning-based edRVFL (WPedRVFL), have shown promising results. In this paper, we introduce two novel WPedRVFL variants that leverage double regularization: 2R-WPedRVFL, which uses separate regularization parameters for input and hidden features, and 1 &2R-WPedRVFL, which dynamically determines the application of double regularization based on dataset characteristics. Experiments on 12 tabular datasets demonstrate the superior performance of 1 &2R-WPedRVFL, showcasing its adaptability and robustness for tabular data classification.