I'm beginning to think that Augusta is written as a mirror to Emma. There are so many similarities and parallels in their attitudes and behaviour:

Both are obsessed with image and surface appearance, as Nncy Ann has pointed out.

Nan Duval has drawn attention to the snobbery of both characters, and their horror of social upstarts and the mixing of ranks.

Both Emma and Augusta are convinced of their own superiority and rightness.

Emma's meddling with Harriet's life correlate's with Augusta's treatment of Jane and her insistence on finding her a place as a governess. In both cases the perpetrator believes she is acting benevolently but is in fact motivated by vanity and ego.

Both characters believe that the Weston's ball at The Crown is held in her honour.

Emma's self-satisfaction at being invited early to approve arrangements at The Crown, and her chagrin when she finds that numerous others have been invited to do the same, are mirrored by Augusta's attempts to organise everything for the Donwell strawberry party and her chagrin when Mr Knightley will not permit her to do so.

Emma's calculated insult to the Martins by enforcing the brevity of Harriet's visit to them correlates with Augusta's glee at her caro sposo's calculated insult to Harriet at the ball (doubtless engineered by Augusta herself).

I expect there are further examples of such mirroring to be found in the text. I wondered about the terms "doppelganger" and "Jekyll and Hyde" to describe this parallelism between the two characters, but I don't think that is quite right, because both these ideas carry connotations of the "good and "bad" aspects of a single character. Emma and Augusta are not opposed in this way, indeed there seems to be remarkably little material difference between them in many of their attitudes and behaviours.

And yet, our hackles rise every time the appalling Augusta opens her mouth, whereas Emma is a much more sympathetic character, forgivable despite her many faults. Perhaps this is because we see Augusta through the eyes of people who find her intolerable, whilst we see the world through Emma's eyes or through the eyes of people who love her. Would Emma seem quite so acceptable if we were only shown her through the eyes of the Martins, Mrs Coles, and Augusta Elton nee Hawkins?