Stanza IX Summary

Get out the microscope, because we’re going through this poem line-by-line.

And I have known the arms already, known them all—
Arms that are braceleted and white and bare
[But in the lamplight, downed with light brown hair!]

Considering how much he dislikes scientific observation of himself, he sure does it a lot to other people. Here he sees women merely as "arms," and he uses the same repetitive phrase about how he has "known them all."
He sounds tired and bored, as if he were saying, "If I have to see one more white arm with a bracelet on it . . .!"
But he seems pretty excited about the arm in line 64. This is probably the arm of the woman he invited on a walk (the "you" of the poem).
If they did go for a walk through half-deserted streets, it would make sense to see her arm under the "lamplight." The soft, "light brown hair" makes this arm different from all the other ones and would seem to contradict his claim to have seen all the arms.

Is it perfume from a dress
That makes me so digress?

Finally! Just when we were wondering where the heck this poem was going, Prufrock admits that he has been "digressing," or wandering away from the main point.
And what is that main point? We’re not sure anymore: that’s how far he has digressed.
He blames his digression on the scent of a woman’s perfume. For a guy that claims to have known all the women, he’s still fairly preoccupied with all things feminine.

Arms that lie along a table, or wrap about a shawl.
And should I then presume?
And how should I begin?

Lots of arms. Loooots of arms. It reminds us of Dr. Seuss's "Green Eggs and Ham." "Did you see them in a shawl? Did you see them down the hall?"
Oh, and in the off chance that you forgot, he still doesn’t know whether he should "presume" to do something.
He still hasn’t told us what that something is. He doesn’t even know where to "begin" talking about it.