Almost all the characters in Persuasion are negatively affected by holding rigid views on English social hierarchy. Jane Austen lived in a time of great flux, when commerce (especially international trade) and industry made some great fortunes but mainly created England's first real middle class.
The traditional aristocracy disdained those without ancient lineage. Sir Walter's haughty disregard for the military is one clear example. He bemoans the idea that men can use it to advance above their station. He states that he objects to the Navy because it can be a means of "bringing persons of obscure birth into undue distinction, and raising men to honours which their fathers and grandfathers never dreamt of."
Lady Russell, in contrast, is able to see value in social mobility, provided that it is accompanied by sufficient wealth. She is really mostly concerned with the material advantages of status.
Anne and Wentworth both suffer the consequences of these limited points of view. Class barriers are often the main cause of Austen's characters' unhappiness, and that is especially pronounced in this novel.