Obesity significantly increases the risk of various diseases, particularly cancers, which present a serious threat to public health. Therefore, identifying cancers related to obesity and exploring their pathological pathways and key genes are highly significant for the prevention and treatment of these cancers. In this study, we propose the obesity and cancer edge connectivity based on expanded modular disease genes and expanded modular networks (OCEC_eDMN) algorithm, which based on the disease-related genes, Biological Process (BP) genes, and Protein-Potein Interaction (PPI) network. The algorithm utilizes Random Walk with Restart (RWR) to expand BP genes and disease genes to generate the expanded modular networks (eMNs) and disease genes (eMDs). Finally, this algorithm calculates the average interaction number between eMDs on eMNs. We utilize OCEC_eDMN to predict the ranking of 12 cancers related to obesity/morbid obesity and obtain an AUC of 0.93/0.84. Additionally, OCEC_eDMN reveals the significant BPs associated with obesity-cancer connections. For instance, "gluconeogenesis" plays a critical role in the connections between obesity and cancers. Through key driver analysis (KDA) on eMDs, we identify the key connectors in obesity-cancer connections. Genes such as GRB2 are instrumental in linking morbid obesity to colorectal cancer in the eMNs of "response to molecule of bacterial origin". The significant eMNs and key genes provide valuable references for the prevention and treatment of obesity-related cancers and carry important theoretical implications.