Catherine Sloper's status as a villain or a hero is considered as well as Dr. Sloper's status.
First, as you examine Catherine Sloper's role as unconventional heroine, you might want to examine her ability to be resilient despite the other dominating characters trying to run her life. Although she is unable to live up to her father's definition of a good or perfect daughter, she is heroic because she eventually finds self acceptance as she recognizes her intelligence. She is also heroic in her ability to display courage as she stands up to her father in her own way.
When looking at her as an atypical heroine, you might also want to mention that she overcomes societal oppression in terms of the push toward the superficial. If you need specific passages to demonstrate her heroism, please note when she says," we can't govern our affections."
Please note also her outer characterization in terms of an atypical heroine. Catherine is plain-faced, not beautiful. Catherine also does not display great ambition but more passivity toward her status. Please observe how Catherine both contradicts and affirms traditional notions of a literary heroine in both her appearance and actions. For example, she lacks social graces and lives with her abusive father. He cruelly assaults her as he says, ...
James' piece 'Washington Square' is explored in terms of character and style.