Sleepless is a tiny snapshot of a bad night and a worse body. The speaker describes "foul weather" that has sunk into the left eye, which sounds like the heaviness and ache of tiredness, as if a storm has settled behind the eyelid. It's a strange, physical way to describe exhaustion, and it makes the weather feel like something happening inside the speaker rather than outside the window.
The poem then moves quickly: writing all night, then going to bed. There's no sense of satisfaction here, only a plain report of what was done. The last lines are the most striking. Only the hands "lie / as a weight," and the word "lie" is doing double work: the hands rest, but they also seem to fail to tell the truth about any ease or peace. Even in bed, the speaker can't let go. The mood is weary, quiet, and a little bleak, the feeling of being worn out but still not at rest.