This data archive accompanies our work, in which we analyze a pseudo-relevance retrieval method that is based on the results of web search engines. By enriching topics with text data from web search engine result pages and linked contents, we train topic-specific and cost-efficient classifiers that can be used to search test collections for relevant documents. Building up on attempts that were initially made at TREC Common Core 2018 by Grossman and Cormack, we address the questions of system performance over time considering different search engines, queries and test collections. Our experimental results show how and to which extent the considered components affect the retrieval performance. Overall, the analyzed method is robust in terms of average retrieval performance and a promising way to use web content for the data enrichment of relevance feedback methods.