The speaker sounds tired, and not from physical effort. The title, "A weariness of the flesh," points to a deeper fatigue, the kind that comes from living among too many words. The opening lines suggest a world full of talk, where all anyone seems to hear is complaint: "an earful of discontent."
Then comes a dull routine. "We go home and to work again" has no drama in it, and the speaker's comment, "how staid," sounds like a sigh, half judging the sameness of life and half judging themselves for sliding into it.
The last image is the most interesting. In the speaker's books, "the weather turns to ink." Real weather, with its wind and rain, becomes printed description. That could be a comfort, a way of escaping into reading, or a loss, since life gets turned into text and kept at a distance. The poem doesn't choose between them. The mood is quiet, restless and a little resigned, like someone gazing out a window while holding a book.