This poem uses the Lamb Meter.
The Lamb Meter type dictates that the first syllable goes unaccented and the second goes accented.
If the poem is read out loud, it could be found that each second syllable from the start has a higher accent that the word prior to them. Having capitalyzed each of the accentuated words in the first verse:
The RAIN set EARly IN to-NIGHT,
The same pattern follows in the rest of the verses.