As we point out in our "Detailed Summary" section, this line contains one of the poem’s many hidden sexual references. On the surface, the meaning of "partial" here is the opposite of "impartial." That is to say, the speaker’s eyes are corrupted by looks that are too much on the side of his mistress. But there’s more here than meets the eye (see what we did there?). The word "partial" in this context could also refer to certain "parts" of the anatomy. Thus, the speaker’s "over-partial looks" could mean "looks that are influenced too much by certain parts of his anatomy." So, you could say that the speaker is warning himself and others not to think with their sex-organs.
Be anchored in the bay where all men ride, (6)
This line contains a crude sexual reference as well—though this time the obscenity isn’t all that hidden. Clearly, the fact that his lady-friend was sexually unfaithful to him has made the speaker feel disgusted with her, which makes him obsessively focused on the "mechanics" of her infidelity.
Why should my heart think that a several plot (9)
As we discuss in our "Detailed Summary," the word "plot" here is actually a metaphor for the speaker’s lady’s genitalia. When the speaker says his heart thinks the plot is "several," he is using this word in the sense of "private" (i.e., the private property of the speaker). As we point out in our opening discussion about the theme of sex, this attitude might indicate some possessiveness on the part of the speaker. More generally, this line shows that the speaker is cool with sex, so long as the "plot" really is "several."
Which my heart knows the wide world’s common place? (10)
But if the "plot" isn’t "several," the speaker won’t be too happy about it. Here, he shows his sexual disgust by means of the literary device known as "hyperbole," exaggerating for effect. It really isn’t possible that the speaker’s lady-friend has cheated on him with the entire world, but when you’re as mad as the speaker is, it sure might seem like it.
And to this false plague are they now transferred. (14)
The speaker’s conclusion contains an incredible complex series of multiple meanings centered on the theme of sexual disgust. These meanings are clustered in two words: "false plague." First of all, the word "plague" might be a reference to the STDs the speaker’s lady-friend has picked up through her "false[ness]," or infidelity. At the same time, as we discuss in our "Detailed Summary," Helen Vendler suggests that the word "plague" might be playing off the word’s Latin root meaning of plaga, meaning "wound."
According to Vendler, the image of a "wound" might call to mind… well, the most intimate part of Shakespeare’s mistress’s anatomy. If you put these two ideas together, you get some sense of the sexual insult the speaker is getting at.