At the end of "Everyday Use," how are the quilts symbolic of Maggie's relationship with Dee?

This is an interesting way to look at the quilts. Symbolism, of course, is defined as a concrete object that represents an abstract idea. In this case, the concrete objects are the family’s antique heirloom quilts Mama promised Maggie would inherit upon her marriage to John Thomas. Dee fusses about this because she wants the quilts for herself; she chastises Mama for thinking of giving the quilts to Maggie, whom Dee says would use everyday until they were reduced to tatters.
In her wisdom, Mama realizes that Dee doesn’t really understand the meaning of the quilts and resolves to give them to Maggie as promised.
Now, if one were to argue that the quilts symbolize Maggie and Dee’s relationship, it’s important to characterize each. At the beginning of the story, Mama says that she believes Maggie has always been jealous of Dee. Maggie seems anxious as they wait for Dee’s arrival, even hesitating to greet her sister. This shows that Maggie is somewhat uncomfortable around Dee.
When Dee visits, she doesn’t seem to interact directly with Maggie at all. This shows that their relationship is definitely not a close one. When she condescends to Maggie about the quilts, Dee reveals her superiority complex: she knows that she is better than Maggie because of her intelligence and acculturation in the modern world outside the isolated lives of Maggie and Mama.
The quilts are described in the story thusly:

In both of them were scraps of dresses Grandma Dee had worn fifty and more years ago. Bits and pieces of Grandpa Jattell's Paisley shirts. And one teeny faded blue piece, about the size of a penny matchbox, that was from Great Grandpa Ezra's unifotm that he wore in the Civil War.

The quilts are clearly very old, and they are made of various pieces and scraps that connect with the family’s history. Dee wants these two quilts because she wants to preserve this history. Maggie, on the other hand, wants to honor this history by using the quilts in the same way that her ancestors did. When Maggie resolves to give Dee the quilts, even though Maggie clearly wants them, this indicates her selfless nature.
Considering these discussions, the relationship between Dee and Maggie is worn and barely stitched together just like the quilts. Maggie is the only one who is willing to concede in order to please Dee, which shows that they’re relationship has always been one-sided.
Mama resolves to give Maggie the quilts not only because she believes Maggie will honor the family’s heritage, but also because she realizes how badly Dee has always treated her sister.