Aunt Jennifer's fingers fluttering through her wool
Find even the ivory needle hard to pull.
The massive weight of Uncle's wedding band
Sits heavily upon Aunt Jennifer's hand.
Aunt Jennifer is attempting to create a work of art that contrasts at every point with the grim reality of her married life. The embroidered tigers are chivalric, certain, proud, and unafraid, whereas Aunt Jennifer is terrified and mastered by her ordeals.
The massive weight of the ring symbolizes the way in which Aunt Jennifer's marriage to a man who frightens her weighs her down and almost prevents her from being creative. The fact that the ring is called "Uncle's wedding band" signifies that, although he gave the ring to her when they were married, it remains his ring. He used it to take possession of her. It is his because she is his.
C.S. Lewis pointed out that we use the possessive form in cases when we do not actually intend to signify possession. When one refers to "their" wife or "their" mother, it is obvious that they are saying these women have specific relationships with them. They are probably not claiming ownership, as in the case of saying "their" car. What Rich subtly does here shows the man's claim to ownership of the woman he married not by saying that she is his (which might have a poetic and romantic connotation) but by saying that the ring with which he claimed her remains his.
Feminist thinkers sometimes object to the symbolism of the engagement wedding ring as a sign of ownership, like the ring a farmer puts through the nose of an animal. This is certainly the case with Aunt Jennifer. She suffers greatly under the dominance of her husband. It is a remarkable feat on Rich's part to convey the suffocating and sinister character of this man in a twelve-line poem, without saying a single thing directly about him.