Anyone who has dragged themselves up a long staircase at the end of a tiring day will recognize the feeling here. The speaker is nearly home, but four flights of stairs still stand in the way. The poem is only three lines long, and it reads a bit like a sigh: there is the effort, the complaint, and then the promise of relief.
The second line carries the weight. Saying each flight is "more tiresome than the last" makes the climb feel like it is getting harder as it goes, as though the speaker's energy is draining step by step. That is a very human exaggeration, and it gives the poem a light, wry tone rather than a truly miserable one.
The last line turns the order of the words around: "then rest I at home." It sounds slightly old-fashioned, and it slows the ending down, almost like the speaker finally sitting down. The mood is weary but patient, with comfort waiting at the top.