When it comes to talking about the theme of revenge in Sonnet 137, things get interesting. That’s because, as far as we can see, the speaker never once mentions the word or concept of revenge. So, why are we bringing it up? Because the poem itself could be interpreted as a form of revenge. Is your mind blown yet? Think about it: would you like to be called "the bay where all men ride" or "the wide world’s common place" or "this false plague"? Probably not. As you can see, writing this poem would be an effective way for the poet to get back at the woman who wronged him.
The fictional speaker of the poem does not intend making these statements as an act of revenge. He's just got some stuff to get off his chest, is all.
If the woman described in the poem is really as bad ("the worst") as the speaker describes her, she's hardly going to be insulted by a poem like this. Revenge: denied!