While there is much debate over the success of trying to determine an author's purpose in writing, with this story, we have the advantage in determining Anne Brontë's purpose as she made a rather clear statement of it in the "Preface" to the Second Edition of The Tenant of Wildfell Hall. She makes it clear that she did write so as to entertain the reader but that she also did have a higher aim. I've added a relevant excerpt from the "Preface" to the question space above.
Anne Brontë makes it quite clear that her purpose was in telling the truth about life among those in her class in relation to marriage and to violence among friends and families. She complains that critics of Agnes Grey and Wildfell Hall said that she was too extravagant in describing parts of life, thus showing them as all out of proportion with reality. Her response is that, in fact, those parts that were criticized are the parts most carefully drawn from real life and rendered with faithfulness devoid of exaggeration:
but when we have to do with vice and vicious characters, I maintain it is better to depict them as they really are than as they would wish to appear. (Anne Brontë, "Preface")
Brontë's purpose, therefore, is to tell the secrets of the lives of "vice" and viciousness that were prevalent but that no one had depicted in the novel to date. Brontë wanted to expose the truth so that the truth might "contribute [her] humble quota towards" the aim of reforming "the errors and abuses of society" as pertaining to the themes of the story.