though some principle of being abides, from which I struggle not to stray. (4-6)
The speaker seems to have found a constant in life that doesn't change with the seasons, but is he struggling against the world or against himself to stay true to it?
and every stone on the road precious to me. (30-31)
A long life can usually lead to two things, either lots of learning experiences or lots of bitterness. In these lines, we see the speaker describing every past happening ("every stone") in his life as something important that has shaped him in some way. He seems to be valuing the past here. Maybe even hard times aren't so bad in hindsight.
a nimbus-clouded voice directed me: "Live in the layers, not on the litter." (35-38)
A voice from the clouds usually means serious business. This particular, and rather wise, voice also says the title of the poem and does that nifty repetition of initial sounds thing (alliteration). We don't see a lot of sound play in "The Layers," so Kunitz is grabbing our attention and directing us towards this significant passage. Perhaps we're supposed to think about layers vs. litter, in vs. on, and how those contrasts relate to humanity as a whole.