What is an "aglet-baby" exactly?

More specifically, from The Stratford Shakspere, ed. by C. Knight (1854)...

The aglet-baby was a small carving on the head of the tag which carried the lace.
Aglet is from the French aiguilletle, a point.

...which I think contextually reflects and amplifies the preceding Marry him to a puppet.

The phrase "Aglet babie" appears in act 1, scene i of The Taming of the Shrew. Grumio's complete response to Hortensio in connection with Petruchio's remark that he seeks a wealthy woman to be his wife is as follows:

Grumio. Nay looke you sir, he tels you flatly what his minde is: Why giue him gold enough, and marrie him to a Puppet or an Aglet babie, or an old trot with ne're a tooth in her head, though she haue as many diseases as two and fiftie horses. Why nothing comes amisse, so monie comes withall.

Here is the entry for aglet-babie in A New English Dictionary on Historical Principles (1888):

Aglet ... 1. The metal tag of a lace (formerly called point), intended primarily to make it easier to thread through the eyelet hoes, but afterwards also as an ornament to the pendant ends. ... 2. Hence, An ornament consisting a. properly, of a gold or silver tag or pendant attached to fringe ; whence b. extended to any metallic stud, plate, or spangle worn on the dress. ... 6. Comb. aglet-babie, ? A doll or (grown-up) baby' decked with aglets. (Explained by some as an aglet shaped like a human figure. Johnson defines aglet as 'A tag of a point curved into some representation of an animal, generally of a man,' but as quotations have been found bearing out this statement, which was perhaps merely hazarded as an explanation of aglet-babie) ...

The notion of an aglet as an ornament is mentioned by an early editor of The Taming of the Shrew in a 1723 edition of Shakespeare's works as follows:

aglet, the tag of a point.

A 1795 annotation of the play has this note:

Aglet-baby, a diminutive being, not exceeding in size the tag of a point; from aiguillettes.

The 1805 Samuel Johnson & George Steevens edition of the play, offers a considerably more detailed gloss on the term:

aglet-baby ;] i.e. a diminutive being, not exceeding in size the tag of a point. So, in Jeronimo, 1605: "And all those stars that gaze upon her face, / Are aglet on her sleeve-pins and her train." Steevens.

An aglet-baby was a small image or head cut on the tag of a point, or lace. That such figures were sometimes appended to them, Dr. Warburton hs proved, by a passage in Mezeray, the French historian:—"portnt meme sur les aiguillettes {points} des petites tetes de mort." Malone.

An 1830 edition of the play, annotated by Samuel Singer, cites the Johnson & Steevens notes but then argues for a contrary reading:

i.e. 'a diminutive being not exceeding in size the tag of a point,' says Steevens; 'a small image or head cut on the tag of a point or lace,' says Malone. It was no such thing; an aglet was not only a tag of a point, but a brooch or 'jewel in one's cap,' as Baret explains it. Am aglet-baby, therefore, was a diminutive figure carved on an aglet or jewel; such as Queen Mab is described:—'In shape no bigger than an agate stone / On the fore finger of an alderman.'

Shakspeare was fond of the image, and refers to it again in Much Ado about Nothing:—'If low, an agate very vilely cut.' And in Henry IV. Part II.:—'I was never mann'd with an agate till now.'

It may be remarked that aglet was also another name for a spangle, as may be seen in Florio's Ital. Dict. in the world tremola ; who also distinguishes the tags of points as long aglets, in the word Puntale. This will explain a passage in Beaumont and Fletcher' Two Noble Kinsmen, Act iii. Sc. 4:—'The little stars and all, that look like aglets' i. e. spangles. And another in Jeronimo, 1605:—"And all those stars that gaze upon her face / Are aglets on her sleeve-pins and her train.'

Several passages in Spenser have been misinterpreted for want of a proper acquaintance with the meaning of aglets.

I don't know what to make of Singer's conflation of aglet with agate, but his note is otherwise quite interesting.

An 1836 edition of The Taming of the Shrew offers this brief note on the meaning of aglet-baby:

An aglet-baby was a diminutive figure carved on an aglet or jewel.

The London Encyclopaedia; Or, Universal Dictionary of Science, Art, Literature, and Practical Mechanics, volume 1 (1829) has this entry for "aiglet or aigle":

AIGLET, or AGLET. Fr. aiguillette, the tag of a lace, or of the points formerly used in dress; sometimes formed into small figures ; spangles &c. [Examples:] "He gyueth alwaye hys old point at on end or other some new aglet ; but when al his cost is don theron, it is not al worth an aglet of a good blewe poynte. [—]Sir Thos. More' Workes, p. 675. c. 2. | It all above besprinkled was throughout / With golden aigulets, that glister'd bright, / Like twinkling stars ; and all the skirt about, / Was hemm'd with golden fringes. [—]Faerie Queene. | He therupon gave for the garter a chain worth 200l, and his gown addressed with aglets, esteemed worth 25l, [—]Mayward. [Citation of the 'aglet baby' line from Taming of the Shrew omitted.]

Samuel Falows, [The Progressive Dictionary of the English Language]](https://books.google.com/books?id=vulBAAAAYAAJ&pg=PA21&dq=%22aglet+baby%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiL6sv44YLsAhVYo54KHRnxBIgQ6AEwB3oECAgQAg#v=onepage&q=%22aglet%20baby%22&f=false) (1835) gives aglet-baby its own entry:

Aglet-baby n. A small image on the end of a lace.

An 1842 edition of the play annotated by J.P. Collier offers this note:

Aglets, or properly aiguillettes, (Fr.) were the ends or tags of the strings used to fasten or sustaain dress. In the 25th Coventry Play, edited by Mr. Halliwell for the Shakespeare Society, p. 241, the devil, disguised as a gallant, says that he has "Two doseyn poyntys of cheverelle, the aglottes of sylver feyn." These aglets not unfrequently represented figures ; and hence Grumio's joke about an "aglet-baby." The strings were themselves often called point, as in the preceding quotation.

Swynfen Jervis, A Dictionary of the Language of Shakespeare (1868) has this entry:

AGLET-BABY. A figure carved on an aglet or tag.

One additional comment on aglet-baby appears in H.H. Crawley's 1891 edition of The Taming of the Shrew:

Aglet-baby. ... Singer says that an aglet was not only a tag of a point, but a brooch or jewel in one's cap. An aglet-baby was therefore a diminutive figure embossed on an aglet or jewel. Baby was used of the reflections of the eyes, and so not unfrequently of these tiny faces or points.

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It is hard to think of a more vivid image of a human being who has been reduced to the status of a trinket that the tiny carved figurine suggested by aglet-baby.

OED:

† aglet baby n. Obsolete

(a) (in Shakespeare) a childish or doll-like person decorated with aglets;

(b) (in later use) used as a vague and sometimes contemptuous term for a small or young person.

Explained by some as an aglet shaped like a human figure. Johnson defines aglet as ‘A tag of a point curved into some representation of an animal, generally of a man’, but no quotations have been found substantiating this statement, which was perhaps merely suggested as an explanation of aglet baby.

a1616 W. Shakespeare Taming of Shrew (1623) i. ii. 78 Give him Gold enough, and marrie him to a Puppet or an Aglet babie, or an old trot with ne're a tooth in her head.

1896 W. Canton W. V. her Bk. 7 Nothing would please her better, could she but dwarf herself into an ‘aglet-baby’, than to climb into those filmy meshes and have a chat in the sunshine with the wily ogre.