In recent years, funding agencies and journals increasingly advocate for open science practices (e.g. data and method sharing) to improve the transparency, access, and reproducibility of science. However, quantifying these practices at scale has proven difficult. In this work, we leverage a large-scale dataset of 1.1M papers from arXiv that are representative of the fields of physics, math, and computer science to analyze the adoption of data and method link-sharing practices over time and their impact on article reception. To identify links to data and methods, we train a neural text classification model to automatically classify URL types based on contextual mentions in papers. We find evidence that the practice of link-sharing to methods and data is spreading as more papers include such URLs over time. Reproducibility efforts may also be spreading because the same links are being increasingly reused across papers (especially in computer science); and these links are increasingly concentrated within fewer web domains (e.g. Github) over time. Lastly, articles that share data and method links receive increased recognition in terms of citation count, with a stronger effect when the shared links are active (rather than defunct). Together, these findings demonstrate the increased spread and perceived value of data and method sharing practices in open science.