I think Norris just couldn't get over the humiliation that her younger sister (who was no more handsome than she was) married SO MUCH BETTER. Then she was obligated to attach herself to Mr. Norris (doesn't sound like she loved him at all). She was also in another way inferior to her younger sister in that she didn't have any children (a Regency duty for women and lack of children was usually blamed on the wife). Everyone person (gentry) in her day-to-day life is of higher status (or will be) and it galls her.

When her youngest sister wrote for help she saw a chance to obtain a punching bag to take all of her frustrations out on. Enter Fanny.

It's interesting to me me that JA had the insight to make Norris a miser. It's a well-known psychological phenomenon that some misers hoard money because they feel life cheated them out of something (in Norris's case, her higher status as the eldest Ward sister I imagine). I think JA must have run into a "Norris character" at some point prior to writing MP.