Cousin Edith isn't the roundest of characters in this book. She's basically a superficial princess who likes to brag about being married and having a beautiful baby. That being said, she and Margaret have a lot of history together. You can see a little bit of competition between them when the narrator tells us, "They had grown up together from childhood, and all along Edith had been remarked upon by everyone, except Margaret, for her prettiness" (1.2).
This comment shows up in only the second paragraph of the book, so it's clear that Gaskell wants us to know two things: Edith is used to compliments, and Margaret isn't the one who's going to give them.
Rather than taking a long time to flesh out Edith's character, the narrator tends to tell us about her directly, saying things like, "[A]lthough she was a spoiled child, she was too careless and idle to have a very strong will of her own, and gave way when she found that her mother had absolutely ordered those extra delicacies of the season" (1.3). So yeah, that's Edith for you: spoiled, pretty, and rich. Yet Margaret likes her anyway. Just goes to show you what a loyal friend Margaret can be.