In Eudora Welty's "Why I Live at the P.O.," we can see jealousy on the part of "Sister." 

It seems pretty evident in that Sister does all she can to discredit her sister, Stella-Rondo when she comes home. Whatever Stella-Rondo says, Sister is there to cast doubt on her:

[Stella-Rondo] says, "Why, Mama, Shirley-T.'s adopted, I can prove it."

... all I says was, "H'm!"

Both Stella-Rondo and her mother believe the comment to be the indication of Sister's disbelief...unsupportive of Stella-Rondo. Stella-Rondo decides to get her revenge by turning Papa-Daddy against Sister by making up a story that Sister thinks Papa-Daddy should cut his beard off. She even manipulates their uncle, Rondo, to become disgusted with Sister.

Sister creates most of her own problems in finding fault with everything Stella-Rondo does:

She's always had anything in the world she wanted and then she'd throw it away. Papa-Daddy gave her this gorgeous Add-a-Pearl necklace when she was eight years old and she threw it away playing baseball...

Obviously, Sister feels that Stella-Rondo has done the same with regard to her husband, Mr. Whitaker:

So as soon as she got married and moved away from home the first thing she did was separate! 

While the circumstances are ridiculous and entertaining, on a more basic level, Sister's responses seem to be generated by her jealousy of her sister—not for the life Stella-Rondo has (her "daughter" and her broken marriage), but her ability to have left their small hometown while Sister remained behind.

As Welty traveled (before writing this short story), she became aware of the very different worlds of life in the North, and life in the South—especially as it still suffered from the damage brought on during the Civil War years, and after. Sister never left home. Her life experience is found at the center of the family unit:

One of the most important aspects of southern identity was the small town and rural lifestyle, with close-knit family and community at its center.

Sister is the one that keeps things going: cooking and caring for the family; her identity is grounded in her position in the home, and her interaction and satisfactory relationships with her family members.

However, some of her tension with Stella-Rondo is based on Stella-Rondo’s wider experiences in the North and her greater sophistication. 

When Stella-Rondo returns home, having experienced the rich and perhaps mysterious life of the North, she upsets the balance of Sister's world. She is able to turn the tables on Sister causing her to suddenly feel disenfranchised in her own home: an outcast.

The resentment Sister feels for Stella-Rondo seems to find its foundation in jealousy for the way Stella-Rondo is wholeheartedly accepted into the family and seemingly favored over Sister. But it may also be because of Sister's jealousy in that Stella-Rondo is more "experienced in the world," having been part of a more complex existence in the North—while Sister has remained behind, unchanged.