1. a cat having a striped or brindled coat; also, a she-cat
2. a spiteful or ill-natured female gossip or tattler
3. an old or elderly maiden lady; an old maid
4. an attractive young woman or girl (slang)
5. a general term for a silk taffeta, apparently originally striped, but afterwards applied also to silks of uniform colour waved or watered
6. a collector's name for two Pyralid moths, the Tabby, Aglossa pinguinalis, and the Small Tabby, Aglossa cuprealis, both with fore wings greyish brown, clouded with a darker colour
7. padding or quilting to improve the figure (obsolete)
8. a concrete formed of a mixture of lime with shells, gravel, or stones in equal proportions, which when dry becomes very hard; originally called 'tabby work'
1. to give a wavy appearance to silk, etc., by calendering
2. to stripe or streak in parallel lines with darker markings
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Definition 5: from French tabis, earlier atabis (both 14th or early 15th c. in Godef.), Sp., Pg., It. tabi, medieval L. attābi (M. Devic in Littré), apparently from Arab. ﻋattābiy, name of a quarter of Bagdad in which this stuff was manufactured, named after 'Attāb, great-grandson of Omeyya. Of this quarter Yule cites from an Arab writer of the 12th c. ‘Here are made the stuffs, called 'Attābīya, which are silks and cottons of divers colours’.
The connection of the other senses is not very clear.
Tabby cat, instanced in 1695, is generally held to have been so named from the striped or streaked colour of its coat. The simple tabby, in the same sense, is much later (1774).
Tabby, old maid, is usually associated with tabby a cat; but it appears earlier, and may have originated as the familiar contraction of Tabitha (cf. Abby for Abigail), as an old-fashioned female name, and have become humorously associated with tabby cat.
It is possible that tabby in the sense of she-cat originated in Tabby for Tabitha; otherwise it is difficult to see any sense-connection between she-cat and brindled cat, since a tom-cat may also be brindled or striped.
Definition 6 (moths) of the noun probably arose from resemblance to the markings of the tabby cat.
The origin of definition 7 (padding or quilting) is very uncertain, and definition 8 (a concrete) may be a different word, though it may also have originated in a fancied resemblance of colour to that of the tabby cat.
From: The Jealous Wife. A Comedy
By George Colman, 1815
Act 2, Scene 3. P. 34