Which of the following events has a profound effect on Cathy and Heathcliff’s relationship?

To answer this question, we need to know the specific events you're referring to in the context of Cathy and Heathcliff's relationship from Emily Bronte's novel "Wuthering Heights". However, there are several key events that profoundly affect their relationship:

1. Cathy's decision to marry Edgar Linton: This decision deeply hurts Heathcliff and creates a rift between him and Cathy. Cathy chooses Edgar because of his social status, despite her deep love for Heathcliff.

2. Heathcliff's disappearance and return: After Cathy's decision to marry Edgar, Heathcliff disappears only to return years later as a wealthy man. His return stirs up old feelings and causes turmoil in Cathy's life.

3. Cathy's death: Cathy's death is a turning point in the novel and has a profound effect on Heathcliff. He is devastated by her death and his life becomes consumed by his desire for revenge.

4. Heathcliff's treatment of Isabella: Heathcliff uses Isabella Linton to enact his revenge, which further complicates his relationship with Cathy, even after her death.

Without the specific events, it's hard to provide a more precise answer. If you could provide the events, I would be able to give a more detailed response.