Then, then, methinks, how sweetly flows That liquefaction of her clothes. (2-3)
Spit it out, buddy. Then what? Then what? In this moment, we really get the sense that the vision of Julia in all her glory has left the Speaker a bit speechless. It's as if the poem is miming at the formal level an experience of awe or astonishment; the Speaker is so amazed he can't even find the right words.
Next, when I cast mine eyes and see (4)
This line emphasizes vision by mentioning the words "eye" and "see." Even though we don't get to see exactly what Julia looks like, we get to see how the speaker feels about what he sees, and what he feels is a sense of amazement at the motion and beauty of Julia's dress.
O how that glittering taketh me! (6)
O, the poetic O. Classic move, Herrick. The interjection of the O at the beginning of the line, in combination with the exclamation point at the end of it, totally make us think this guy is amazed at how Julia's clothes have such a powerful effect on him.