The wedding band is pretty much the opposite of Aunt J's tigers. The tigers are prancing and free, while the wedding band is heavy and holds Aunt J back from the life she'd like to lead. There's a push-and-pull effect in this poem between the freedom of the tigers and the limitations of the wedding band. And, of course, the wedding band itself isn't what's holding Aunt Jennifer back from life. The wedding band represents Aunt J's unhappy marriage, and, on a larger scale, the patriarchal (male-dominated) society that she lives in.
Lines 5-8: The speaker tells us that "the massive weight of Uncle's wedding band" makes Aunt Jennifer's needlework difficult to complete. It's hard for her to pull the needle, and her hands flutter in fear or hesitation. Of course, it's not the actual band that's making her afraid, but everything that the band symbolizes: her marriage, her husband, and the patriarchal society that limits the freedoms of women.
Lines 9-10: Even in death, the speaker imagines that Aunt Jennifer will experience the pain that the symbolic wedding band has caused. She will be "ringed with ordeals she was mastered by." Though the poem isn't explicit about the difficulties of Aunt J's life, it does describe them with the vocabulary of marriage (i.e., the wedding ring). We can thus infer that Aunt J has been terrified by the reality of her marriage, which has "mastered" her, and probably taken away her agency (her ability to control her own life and make her own decisions).