How does having a female author affect the plot of Silas Marner?
An author's gender doesn't necessarily impact the plot of any novel; after all, gender is a social construction, and imagination knows no bounds. Unless you found yourself remarking, "I can tell this novel was written by a woman" when reading, the question you pose is difficult, if not impossible, to answer fairly.
Consider that even today, authors often use gender neutral pseudonyms to prevent social constructions about gender from impacting readers' reactions to their work. For George Eliot, the pen name of Mary Ann Evans, a male-gendered pseudonym increased the likelihood of her fiction being taken seriously; it also kept her fiction writing separate from her work and from her life.
It is interesting and often fruitful, however, to ask if an author's life influences how they represent certain events. How does their interaction with the world impact how they portray divisions between genders, social classes, races, and the like? These are all good questions to consider, particularly when examining nineteenth-century literature.
Consider that Eliot was a well-educated woman and a noted journalist and editor. Her social status and education enables her to understand how the world works; she didn't live as a cog in the industrial machine. Eliot understood the complexities of the world, and that's evident in her novels, with her depictions of the industrial age and the divisions between social classes. She creates layered narratives, like Silas Marner, that both represent the world and instruct (or inspire) the readers. For example, on one hand, Silas Marner functions as a morality tale, asserting that love and hope wins, and on the other it's a study of the function of community and of a world that is swiftly changing.
The gender of the author has no obvious effect on the plot of a story. George Eliot spent much of her career fighting against precisely that sort of stereotyping. In fact, one might argue that both her use of a male pseudonym and her erudite, rational narrative style are deliberate attempts to avoid being seen as part of what Hawthorne described as "a damned mob of scribbling women."
Rather than writing in a traditionally "feminine" genre such as the Gothic aimed at a female audience, Silas Marner has a male hero and addresses issues of religion and social justice.
The part of Eliot's biography that most obviously influences the plot of the story is not gender but religion and region. Eliot was brought up in the Midlands and many of her works, including Silas Marner, focus on the conflicts between dissent and Establishment and religious ideals and realities in the small towns of that region.