The poem repeats several words/phrases for the purposes of emphasis and contrast. For example, the word "heart" occurs in lines 3 and 10, and in line 12 as "heart's." Not only does the repetition stress that this is a love poem—albeit a slightly twisted one—but it also draws out the contrast between the speaker's "foolish" heart and his lover's "proud" one. This is a poem not only about the love but about the tension between hearts, as well as the tension within the speaker's own heart.
Repetition also draws out the contrast in line 9:
But my five wits nor my five senses can
Dissuade one foolish heart from serving thee,
In the Europe of Shakespeare's day, some thinkers believed that the five bodily senses (sight, hearing, touch, taste, smell) had their equivalent in the mind. These five mental faculties, or "wits," were said to be common wit (i.e., common sense), imagination, fantasy, estimation (i.e., calculation), and memory. Here, the repetition-with-variation—"my five wits nor my five senses"—stresses that neither the speaker's physical perceptions nor his mental processes can help him in his lovesick state.
Finally, the word "Nor" itself occurs several times, not only in line 9 but in the anaphora of lines 5-7:
Nor are mine ears with thy tongue's tune delighted,
Nor tender feeling, to base touches prone,
Nor taste, nor smell, desire to be invited [...]
In a sonnet written centuries after Shakespeare, Elizabeth Barrett Browning famously "count[ed] the ways" in which she loved her partner. Here, it's as if the speaker is counting the ways in which he doesn't love his partner! The succession of "Nor"s emphasizes that he doesn't love her through any of his senses—not hearing, nor touch, nor taste, etc. Of course, all of this sets up the claim that he does love her with his heart.