There is actually no difference of class between Kate and Marlow's family. Mr. Hardcastle, Kate's father, clearly indicates that Marlow emerges from the same social class as himself and his daughter in Act I scene 1 when he tells his daughter about Marlow, the man he wants her to marry:
Mr. Marlow, whom I have pitched upon, is the son of my old friend, Sir Charles Marlow, of whom you have heard me talk so often. The young gentleman has been bred a scholar, and is designed for an employment in the service of his country.
Later on Marlow himself describes Kate as being "well-bred and beautiful," again indicating that she is a gentlewoman and of the same class as himself. Perhaps the difficulty in this play lies in recognising the importance of one of the key themes which is appearances vs. reality. A key part of the comedy is that Kate appears to be a serving maid to Marlow, and deliberately disguises herself as such, because she discovers that as a maid he is able to respond to her freely and without bashfulness. However, this is just an act, and is not her proper station in life, which is a gentlewoman, and of the same class and rank as Marlow himself, making this a very fitting marriage.