Mrs Elliot could have been of inferior birth but respectable family. Maybe Mrs Elliot's father was a prosperous tradesman or merchant who left money which enabled her to 'marry up' ? In P&P, Miss Bingley's fortune came from trade and Louisa had married a gentleman with a townhouse.
People in JA's time did advance through trade into genteel society. I doubt acquisiton of wealth always meant higher social class.
However, an interesting thought Mrs Elliot was a monied widow who attraced William Walter for sake of independence; I'll watch for any evidence in text. :)