Eleanor Tilney is arguably the most serious character in the book, on two levels. On the one hand, she is serious in terms of personality. She's polite and earnest and maybe just a little boring. On the other hand, her life circumstances are also serious. Her mom died when she was young and her dad is a bit of a control freak. But at least a Viscount magically drops from the sky for her to marry at the novel's end, which conveniently allows the people in whom we have a more vested interest (Henry and Catherine) to get married.
If that's all sounding a bit familiar, it might be because Eleanor perfectly fits the criteria for a heroine that Jane Austen outlines at the beginning of Northanger Abbey. We've got the family tragedy, the loss of a mother, a somewhat villainous patriarch, a creepy setting (the Abbey), a mysterious star-crossed love, years of suffering and trial, etc.
So why is the novel's protagonist and ostensible heroine, Catherine, classified as anything but a heroine? And why does Eleanor Tilney, a somewhat dull secondary character, epitomize a Gothic novel heroine as described by Austen? Well, this might be because Austen is poking fun at the Gothic novel. By having Eleanor, a nice if somewhat uninteresting character, perfectly match the criteria for a Gothic novel heroine, Austen might be implying that Gothic novel heroines are overrated and a bit boring when compared to more dynamic characters like Catherine. Eleanor's personality doesn't appear to alter much at all over the course of the text, unlike Catherine, who evolves.
Aside from making a subtle and satirical point about the Gothic novel, Eleanor also contrasts with Isabella Thorpe. Eleanor and Isabella are both Catherine's friends and the younger sisters of Catherine's two love interests. So Eleanor has a vital position in the novel's sibling structure, where three contrasting pairs of brothers and sisters interact.
Catherine, who grows up considerably over the course of the novel, eventually drops her superficial friendship with Isabella in favor of a more mature friendship with Eleanor. In many ways, the mature and reasonable Eleanor represents the type of adult that Catherine makes some progress towards becoming. Eleanor is, after all, rational, kind, well-mannered, well-read, and is capable to keeping up with her brother's wit. And if she's not as exciting and wildly entertaining as Isabella, well, that's probably a good thing. After all, she does get rewarded with her very own Viscount in the end, which just proves that good deeds, like putting up with her difficult father, really can be rewarded.