Dee wants the old quilts for several reasons but mainly because she wants to display them as part of her "heritage" in her home in the city. She does not believe that they are appreciated in the country with Maggie and Mama because they actually use the quilts. For the two older women, heritage means passing down skills and practical heirlooms to the next generation. When Maggie thinks of the quilts, she remembers how she was taught to make them and uses them because she believes that that is what her grandma would want her to do. In contrast, Dee believes that the quilts should be displayed rather than used so that they will last and be able to be passed on for many years. While her desire to have the quilts certainly comes across as selfish and condescending toward her sister, I think that Walker uses Dee to demonstrate that humans (even within the same family) have different definitions of heritage and what it means to honor one's ancestors and culture.
In the short story "Everyday Use" Dee has left home and gone on to become more successful. She has re-established her identity by looking back towards her black heritage. For example, she has changed her name to Wango.
Dee sees the quilts as a monetary representation of the past. She takes pictures of the house with its tin roof and comments on the bench that has been rubbed inward through years of rumps on it. Yet, Dee misses the real meaning of the quilt. She talks about the squares and what they are made from, but really does not know that each one is also made from something else. In her effort to know her heritage she tends to overlook the beauty of her heritage.
Dee wants the quilts to display in her home as a proud representation of her heritage. However, if it were not a fashionable thing, Dee would not even want the quilts, so in a way it is also a fashion statement more than about her need to capture her heritage.