What is Mr. Guppy's interest in revealing the connection between Esther and Lady Dedlock? Why does he persist in getting involved?

Mr. Guppy is hoping that, if he can draw a connection for Esther to her real mother, she might reconsider his proposal of marriage. He is also interested in letting Lady Dedlock know that he is aware of her affair with Hawdon and now can hold this over her head. He claims to have letters that will prove his claim.