The speaker is drifting through the streets with no task except thinking, and even that happens "outside," as if thought belongs to open air and freedom. It's a picture of idle, unhurried life, the kind of curiosity an amateur has, doing something for its own sake rather than for pay or status.
Then the tone shifts. The speaker "weathers" themselves, a word that suggests being worn down slowly, like a stone or a wall left in the rain. The result is a heavy sleepiness, eyes that won't stay open. That tiredness leads to the poem's grim last move: the speaker "must be buried / in some profession." Burial and career are joined, so taking a job feels like a small death. The title makes this explicit, since the amateur dies when the professional takes over.
The mood is quiet, weary and a little darkly funny. The speaker doesn't rage; they seem to accept that time and necessity will wear down their free wandering.