In the poem, we are given Miss Rosie's present before we know her past. Now, she is an impoverished, feeble old woman. When we learn that she "used to be the best looking gal in Georgia," readers are surprised. We are even more surprised when the speaker states, "I stand up/ through your destruction/I stand up."
Your two questions are related. Miss Rosie obviously represents more to the speaker than merely an old lady surrounded by "too old potato peels." What she symbolizes to the speaker causes the speaker to "stand up." These lines seem to indicate respect for Miss Rosie. We stand up for another person out of respect. Perhaps the speaker respects Miss Rosie's history and feels pity for her decline. Perhaps the speaker respects the fact that she has had to endure such hardships. Perhaps the speaker is standing out of respect for Miss Rosie's survival.
I think it important to note that Miss Rosie's is sitting, a fact that is mentioned twice. This contrast between Miss Rosie's sitting and the speaker standing is quite obvious. This contrast leads us to speculate about others. The speaker may be young and successful, and she knows that she is only successful through the hardships that the previous generation has had to endure. Through Miss Rosie's destruction, the speaker is able to stand tall. Standing up may be a salute.