Whenas in silks my Julia goes, Then, then, methinks, how sweetly flows (1-2)
Just like line 4, this line emphasizes the "I," the speaker who's viewing the scene. We can hear "I" in "my" and in "methinks," too. So really we can't be sure of anything he's describing because we're looking at the world through Herrick-colored glasses.
Next, when I cast mine eyes and see (4)
This is a particularly self-centered line; notice that sequence in the middle, "I," "mine," and "eyes." We can hear "I" in "eyes" and "mine," in such a way that we can no longer doubt who's really doing the seeing. This is all about the speaker's version of reality—not reality itself. This playfulness emphasizes the singularity—the fact that they belong to one particular person—of all the images in the poem.