LOUISE: I find your mother completely fascinating.
RORY: Funny – so does she.
LOUISE: It’s almost more like having a big sister.
Amy Sherman-Palladino reportedly wrote Lorelai and Rory to have a relationship that was more sisterly than like mother-and-daughter. Sherman-Palladino had a sister who died very young, and her imaginings of what their relationship might have been like (best friends who looked alike) was part of the basis for that between Lorelai and Rory. She also thought that if she ever had a child, she would want to be more like a friend than a parent, so that was another imagining which went into the relationship between Lorelai and Rory.
The Annotated Gilmore Girls 