A Brig is a two-masted ocean-going vessel. It’s not a “little” craft, but the poet-speaker says she “knew” it.  She accordingly uses an affectionate diminutive in telling what her storm-tossed friend went through, becoming “delirious” and longing like a sleepless invalid for night to be over.  
 
In the next stanza, no ship appears. All four lines are taken up with a simile, one term of which is a person who “slipped,” ”stept,” “tripped,” “dropped” like a drunkard, and, oddly, has “a white foot” (a stocking? a wave?). By the time he or she drops away, we have all but forgotten the first term of the comparison, the Brig.
 
It takes the shocking first line of the third stanza, “Ah, Brig – Good Night,“ to remind us of the storm-tossed ship. The drunken person of the second stanza has dropped into the sea carrying the Brig and its crew along.
 
As if their fate were not enough to animate a 12-line lyric, the poem adds a devastating twist: We may pity the lost Brig and, perhaps, the drunkard, but the Ocean remains, at Heart, indifferent to both. Like most personal misfortunes, this one touches the victim’s immediate surroundings, while the center remains “smooth,” and “Blue” (not green or black like real waves at night). This is a story of some private agony essentially unseen (“dropped from sight”) and left un-mourned.
 
“Tossed and tossed,” “spun and spun,” “slipped and slipped” are patterns, established and  subtly disrupted. This typifies the poet’s technique here. For example,  2, 3, 4, and 5-stress lines alternate with the fluidity of a modernist poem. As for the sound system. In the first stanza, where we might expect lines 2 and 4 to rhyme like a hymn or like many of Dickinson’s other poems, there is no end-rhyming at all. The music is created by a consonance of s-clusters (“tossed,” “Blast,” “spun”) continued in stanza 2 with “slipped.”  
 
The only full end-rhyme in the poem serves to bind together the middle and final stanzas: “Sight,” ends the last line of stanza 2.  “Good-night” ends the first line of stanza 3. Speaking of rhyme, we find in the last four lines, not only an abundance of internal echoes—“crew,” “You,” “too smooth,” “Blue” — but also an end-rhyme of “You” with “You,” an identical rhyme, often considered a technical blunder, one that the poet could surely have avoided, but this recurrence serves to draw You, reader, further into the sad events. 
 
To see the toy boat come to grief arouses pity for the crew and the unnamed, delirious person—perhaps the poet herself, whose sufferings are insufficiently recognized in the unruffled New England surroundings. For her sake, I feel a momentary pang at the death of the Brig.  But what really breaks my heart in this brave “little” poem is the utter perfection of its composition.