Etymology of Sleep like a Top

The phrase sleep like a top appears in The Two Noble Kinsmen by John Fletcher and William Shakespeare, which was first performed in 1613–14, and published in 1634.

There is a possible clue to the etymology in The Countesse of Pembrokes Arcadia, Volume 2 (somewhere between 1580 and the author's death in 1586) By Sir Philip Sidney, in which the phrase like a toppe is used to express the stationary nature of a top, which can only be moved by whipping it.

Griefe onely makes his wretched state to see
(Even like a toppe which nought but whipping moves)

From this, I believe it might be possible that it is the stationary nature of a top, which requires whipping to move, or wake, it that gives rise to the phrase sleep like a top.

Here is a different claim about the origin:

Sleep like a top. When peg-tops and humming-tops are at the acme of their gyration they become so steady and quiet that they do not seem to move. In this state they are said to sleep. Soon they begin to totter, and the tipsy movement increases till they fall. The French say, Dormir comme un sabot, and Mon sabot dort.

Repeated here:

Sleep like a top.Tops, or more correctly spinning-tops', were popular amusements in the days before children had access to toys requiring batteries. The British Museum has on display tops from Egypt, dating from around 1250 BC. When a top is spinning well the precessional effect causes its axis to remain stationary and it can appear to be still, that is, 'sleeping'.

The expression 'sleep like a top' is quite old and is recorded from at least 1693, when it appeared in William Congreve's The Old Batchelour:

It appears the that there is no agreement on the origin of this saying.

In Balzac's Pere Goriot (1835) the following appears "voilà Christophe qui ronfle comme une toupie." (There's Christophe snoring like a top). So in this case it seems to be the noise a spinning top makes not its stillness that is important.