Vanity was the beginning and the end of Sir Walter Elliot's character; vanity of person and of situation. He had been remarkably handsome in his youth; and, at fifty-four, was still a very fine man. Few women could think more of their personal appearance than he did, nor could the valet of any new made lord be more delighted with the place he held in society. He considered the blessing of beauty as inferior only to the blessing of a baronetcy; and the Sir Walter Elliot, who united these gifts, was the constant object of his warmest respect and devotion. (1.6)
Sir Walter's two favorite aspects of himself are rather similar: both beauty and rank are things he was born with and didn't have to work for (Gowland's face cream aside).
[Sir Walter speaks] "It cuts up a man's youth and vigour most horribly; a sailor grows old sooner than any other man. I have observed it all my life. A man is in greater danger in the navy of [...] becoming prematurely an object of disgust himself, than in any other line. [...] I shall not easily forget Admiral Baldwin. I never saw quite so wretched an example of what a sea-faring life can do; but to a degree, I know it is the same with them all: they are all knocked about, and exposed to every climate, and every weather, till they are not fit to be seen. It is a pity they are not knocked on the head at once, before they reach Admiral Baldwin's age." (3.16)
Sir Walter's ultimate beauty regime: assisted suicide when you're too old to be pretty. While he's (hopefully) exaggerating at least a little, the fact that he would joke about killing ugly people so he doesn't have to undergo the pain of looking at them is revealing of his character.
"There is hardly any personal defect," replied Anne, "which an agreeable manner might not gradually reconcile one to."
"I think very differently," answered Elizabeth, shortly; "an agreeable manner may set off handsome features, but can never alter plain ones. (5.15-16)
And there we have Anne vs. Elizabeth in a nutshell: one places character first, while the other says it all comes down to appearances. Both, however, agree that appearance matters in judging people, so perhaps they're not that different after all.
"Altered beyond his knowledge." Anne fully submitted, in silent, deep mortification. Doubtless it was so, and she could take no revenge, for he was not altered, or not for the worse. [...] No: the years which had destroyed her youth and bloom had only given him a more glowing, manly, open look, in no respect lessening his personal advantages. She had seen the same Frederick Wentworth. (7.34)
Anne sees the change in her own position as an outward sign of her inner sadness; one could expand from that to say that Wentworth hasn't been as full of regrets as Anne, and that's why he looks so good. But it comes out later that he's been just as upset about the way things went as she was – so why doesn't that show in his looks the way it does for Anne?
"He [Mr. Elliot] looked at her [Anne] with a degree of earnest admiration, which she could not be insensible of. She was looking remarkably well; her very regular, very pretty features, having the bloom and freshness of youth restored by the fine wind which had been blowing on her complexion, and by the animation of eye which it had also produced. It was evident that the gentleman, (completely a gentleman in manner) admired her exceedingly. Captain Wentworth looked round at her instantly in a way which shewed his noticing of it. He gave her a momentary glance, a glance of brightness, which seemed to say, "That man is struck with you, and even I, at this moment, see something like Anne Elliot again." (12.6)
It takes Mr. Elliot's gaze for Wentworth to realize that Anne's getting her looks back – in this matter he's persuaded by another's opinion rather than by his own independent judgment.
He did justice to his very gentlemanlike appearance, his air of elegance and fashion, his good shaped face, his sensible eye; but, at the same time, "must lament his being very much under-hung, a defect which time seemed to have increased; nor could he pretend to say that ten years had not altered almost every feature for the worse. Mr Elliot appeared to think that he (Sir Walter) was looking exactly as he had done when they last parted;" but Sir Walter had "not been able to return the compliment entirely, which had embarrassed him. He did not mean to complain, however. Mr Elliot was better to look at than most men, and he had no objection to being seen with him anywhere." (15.12)
At last we see that Sir Walter has principles – he won't make the polite reply if he doesn't believe it. This also suggests that he believes wholly Mr. Elliot's remark that he hasn't changed, and doesn't in the least suspect that Mr. Elliot might not mean it.
[Sir Walter speaks, even though it's in the third person] "The worst of Bath was the number of its plain women. He did not mean to say that there were no pretty women, but the number of the plain was out of all proportion. He had frequently observed, as he walked, that one handsome face would be followed by thirty, or five-and-thirty frights; and once, as he had stood in a shop on Bond Street, he had counted eighty-seven women go by, one after another, without there being a tolerable face among them." (15.13)
Sir Walter cares way too much about this, if he actually takes the time to keep a tally of pretties vs. uglies. Why is he so invested in this? Handsome guys he might feel personally threatened by, but why is he so obsessed with unattractive women?
It is something for a woman to be assured, in her eight-and-twentieth year, that she has not lost one charm of earlier youth; but the value of such homage was inexpressibly increased to Anne, by comparing it with former words, and feeling it to be the result, not the cause of a revival of his warm attachment. (23.66)
Beauty is in the eye of the beholder – where have we heard that before? Wentworth's opinion is just as much a judgment of him as of Anne – at least it is in Anne's interpretation that she's pretty because he loves her for her, not because he cares so much about appearances that her beauty made him love her again.
Glowing and lovely in sensibility and happiness, and more generally admired than she thought about or cared for, she had cheerful or forbearing feelings for every creature around her. (23.76)
Both Anne's previous plainness and her re-blossoming into beauty suggest that happiness is a major factor in how attractive someone looks – and being unconscious of one's own beauty doesn't hurt either.
Sir Walter, indeed, though he had no affection for Anne, and no vanity flattered, to make him really happy on the occasion, was very far from thinking it a bad match for her. On the contrary, when he saw more of Captain Wentworth, saw him repeatedly by daylight, and eyed him well, he was very much struck by his personal claims, and felt that his superiority of appearance might be not unfairly balanced against her superiority of rank; and all this, assisted by his well-sounding name, enabled Sir Walter at last to prepare his pen, with a very good grace, for the insertion of the marriage in the volume of honour. (24.2)
Sir Walter's two obsessions come together in the marriage of Anne and Wentworth. While others think it's all right for the rich and the talented to have upward class mobility, Sir Walter thinks being beautiful is reason enough to be accepted in society. Does this contradict his class snobbery, or reinforce it?