Teresa turns anxiety into an unwanted suitor. Worry is a man who keeps pursuing her, circling her like a partner on a dance floor, even though she has made it clear she isn't interested. The joke is that he never takes the hint, and the longer it goes on, the more tiring it becomes.
The comparison works because Worry is such a bad boyfriend. He doesn't compliment her or hold her at night and promise things will be fine. He gives her knotted stomachs, lost sleep and a heap of stress to carry each morning. She contrasts this with the life she had before, when she felt happy and free, and with the man she truly loves.
The mood starts out weary and a little desperate, but there's a turn near the end. She finally announces, "I'm calling it quits!" and the tone becomes firm, even defiant. Still, the last lines are honest: she knows Worry will return, so she asks him to pretend not to know her.