Austen's characterizations help to show that what she considers an attribute of high social class, is not necessarily physical beauty, but beauty in mind and character.
In the cases of Sir Walter Elliot and his eldest daughter Elizabeth, beauty was both innate and connected with social class, at least in terms of physical beauty. However, Austen does attribute very ugly characteristics to both of them. For instance Sir Walter is not only handsome, he is also described as an excessively vain man. In fact, "Vanity was the beginning and the end of [his character" (Ch. 1). In other words, his only character trait is vanity. Not only is he so vain as to devote all of his spare time to reading his recorded life in the Baronetage, he also pays more attention to his appearance than "few women" would (Ch. 1). In Sir Walter's eyes, due to his vanity, beauty and social class are the only two things of value. However, while he may have been born with beauty, his social class has done nothing to improve the beauty of his character.
Even Elizabeth is described as being as vain and extravagant as her father, she is also very unpleasant towards Anne. While even at the age of 29 she is still very handsome, like her father, her social class has done nothing for the beauty of her character.
Anne, on the other hand, is described as having a very noble character. She is intelligent, sensible, and very caring. However, due to misfortune, while she was once very pretty, she lost her good looks early and is now very plain. While Sir Walter would argue that Anne's looks have no place in his upper class society, Anne's nobleness of character show that, despite what Sir Walter thinks, good looks should not be as much a part of high social class as nobleness of mind and character.