The couplet "But if you want to stay around and love me / You know it's alright with me" recurs at the end of each verse, providing a sense of the constancy of "stay[ing] around."
The rhyme scheme of the verses is AABB (if rhyming "me" with itself counts), but in the bridge, this is replaced with ABA ("I'm sick and tired of being on my own / But you know I'll take nobody / Who's gonna leave me tired and alone"). Unlike in the verses, the sequential lines don't rhyme, so there's a sense of the isolation of "being on my own."
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*As I've noted before, though, the version of "I Want You Back Again" on Still Got That Hunger is in D minor.