In just five short lines, the speaker describes what they do: "My office: wit." Their job, or duty, is to be clever, to chant and talk, and what they talk about is "the weight of age." So the speaker seems to be someone who turns heavy subjects like aging and time into words, perhaps into poems.
The final lines carry the twist. "Where I err / is the present." The speaker makes mistakes not in the past or the future, which are easy to talk about, but in the here and now. All that chanting about age may keep them from actually living in the moment.
The title helps. "Poetic fallacy" suggests a trick of language, a false note. The mood is dry, a little rueful, and quietly self-aware. The speaker seems amused at their own habit, but there is also a hint of loss in it: words can describe time, yet they may miss the moment slipping by.