Class is a persistent subtext in the novel, and Austen is keen on linking money and marriage in the many relationships. Class in England is far more than wealth, and the markers of class suggest power and privilege. Indeed, Elizabeth's claim that she is of equal class to Darcy is a point she insists on in her argument with Lady Catherine. Her unwillingness to be intimidated by Darcy or Lady Catherine does speak to her sense of social value, despite her relative poverty. The perceived slight Darcy makes toward her both at the dance and in his proposal is wounding because it speaks to the limitations a perceived member outside the gentry would face as a marriage prospect. Even Mr. Collins cushions his proposal in terms of Elizabeth's assumed desire to make a match that allows her to maintain or improve her class.
A word on how readers of the day might parse out the different types of class is as follows:
Lady Catherine holds a title, as the daughter of an Earl. Darcy's mother would also then have been daughter to this same Earl, making his maternal grandfather among the peers of England, or the upper class. His father, however, was not so titled but belonged to the landed gentry. Darcy's father "married up" in class, but Darcy does not inherit his mother's title. Elizabeth's father "married down" in class, but while there is a difference in wealth between Mr. Bennet and Mr. Darcy, they belong to the same class.
Mr. Collins, while seemingly of the same status as Mr. Bennet, will become landed gentry when he inherits Longbourn, though his status as a vicar puts himself among those who practice a gentlemanly profession, of which the law, the clergy, medicine, and the military were the four allowed.
Charlotte's father, however, is a knight, though his title is not one of inheritance, even if he had a son to give it to. Because Sir William made his money in trade but was rewarded his knighthood for service as a mayor, Charlotte is marrying up in accepting Mr. Collins. She gains not only the security of avoiding spinsterhood and financial comfort but also a status upgrade. Mr. Gardiner also works for his living as a lawyer. In Regency England, working for a living is not something the upper or noble class would do. Mr. Darcy's deference to him at the end of the novel is meant to show his appreciation of character more than class.
Mr Bingley and his sisters are wealthy but the children of a man in trade. Caroline's eagerness for Charles to buy an estate is based on her desire to slough off her family's status as people of trade and to join the landed gentry. Technically, that suggests that he will become a social equal to Jane Bennet, though her poverty and her inability to inherit land would never place her above the Bingleys.