In the field of information retrieval, query expansion (QE) has long been used as a technique to deal with the fundamental issue of word mismatch between a user's query and the target information. In the context of the relationship between the query and expanded terms, existing weighting techniques often fail to appropriately capture the term-term relationship and term to the whole query relationship, resulting in low retrieval effectiveness. Our proposed QE approach addresses this by proposing three weighting models based on (1) tf-itf, (2) k-nearest neighbor (kNN) based cosine similarity, and (3) correlation score. Further, to extract the initial set of expanded terms, we use pseudo-relevant web knowledge consisting of the top N web pages returned by the three popular search engines namely, Google, Bing, and DuckDuckGo, in response to the original query. Among the three weighting models, tf-itf scores each of the individual terms obtained from the web content, kNN-based cosine similarity scores the expansion terms to obtain the term-term relationship, and correlation score weighs the selected expansion terms with respect to the whole query. The proposed model, called web knowledge based query expansion (WKQE), achieves an improvement of 25.89% on the MAP score and 30.83% on the GMAP score over the unexpanded queries on the FIRE dataset. A comparative analysis of the WKQE techniques with other related approaches clearly shows significant improvement in the retrieval performance. We have also analyzed the effect of varying the number of pseudo-relevant documents and expansion terms on the retrieval effectiveness of the proposed model.