It is easier to sympathise with Maggie than with Dee in their conflict over the quilts. Maggie has not had the chances in life that Dee has had; she has not gone out in the world or had much of an education. It seems she has never pushed herself forward made demands for herself, as Dee so emphatically does. Dee appears overbearing and quite aggressive, and thus the reader tends to side with the unobtrusive Maggie.
When Dee insists on having the quilts Maggie simply gives in. Her mother observes that 'this was Maggie's portion. This was the way she knew God to work'. Maggie, then, appears humble and submissive, ready to yield to others rather than to fight her corner. It seems she has always been this way: this is her fate, her 'portion'. Her mother, however, intercedes for her on this occasion, snatching the quilts away from Dee to give to her.
The reader feels that Maggie deserves her moment of triumph, although typically, she doesn't make a show of it as Dee would have done. Dee also shows herself to be quite ungracious when she can't have her own way, almost like an angry and sulky child. This also makes the reader feel less inclined to side with Dee than with Maggie.
We are also assured that Maggie will make proper use of the quilts - 'everyday use', to quote the title, whereas Dee seems to want them just to show off, to put on display. This is another reason why Maggie's claim to the quilts tends to attract more sympathy than Dee's.