This pattern that other editors have identified—one line in iambic tetrameter (four feet, each having one unaccented syllable followed by one accented syllable), followed by one line in iambic trimeter (three feet, each having one unaccented syllable followed by one accented syllable)—is actually referred to as Common Meter. Common Meter, as a rule, retains iambic strictness; there is no irregularity, and so it can sound very formal and even straightforward and simple.
Common meter is the rhythm used in the hymn "Amazing Grace," and one can actually even sing this poem to the tune of "Amazing Grace"; if you do this, you'll see how the rhythms of the two texts perfectly align. Dickinson plays a little bit with this structure, as it is typical for there to be end rhyme in lines 1 and 3 of each stanza as well as in lines 2 and 4. She does not employ perfect rhymes—though there are often other sound similarities at the ends of lines—until the final stanza. There, she rhymes the final word of line 2, "me," with the final word of line 4, "see," giving the poem a sense of closure that it has lacked up until now as a result of her refusal to use perfect rhymes despite her embrace of perfect meter.