From etymonline.com:
tad (n.)
1877, “young or small child,” probably a shortened form of tadpole, which is said to be the source of Tad as the nickname of U.S. President Lincoln’s son Thomas (1853–1871). The extended meaning “small amount” is first recorded 1915.
Since he died decades before I’d even heard of him, I never got to see jazz pianist, composer and band-leader Tadd Dameron perform. As a consequence I am unable to say – Wikipedia having shed no light on this aspect of the man – whether he was of small (or for that matter unusually large) stature, and as a further consequence whether this is how he acquired the “Tadd” moniker.
Especially when a stronger explanation can be derived from his full name of Tadley Ewing Dameron. It’s unlikely, therefore, that ‘Tadd’ has anything to do with his height, be it short or – in the ironic vein which gave us Little John, Tiny Rowland and the Tiny Montgomery of whom Bob Dylan sang so menacingly on The Basement Tapes – the very opposite.
As for the etymology of tad, a plausible explanation is that it’s an abbreviation of tadpole. Says Grammarphobia.com:
…“tadpole” is interesting too. It combines the Middle English word tade or tadde (toad) and, apparently, the noun “poll” (head or roundhead.) It was first recorded in the 1400s, the OED says, as “taddepol.”
“Tad” first cropped up in 1845 with a different, unrelated meaning: someone who can’t or won’t pay. But the modern sense of something small was first recorded in the 1870s, when a “tad” or a “little tad” meant “a young or small child, esp. a boy,” the OED says.
It wasn’t until the 20th century that “a tad” came to mean a small amount or, used as a modifier, a little, slightly, or somewhat.
The OED’s first citation is from a 1940 issue of the journal American Speech, in an article about Tennessee expressions. The article said “tad” meant “a very small amount,” as in the sentence “I want to borrow a tad of salt.”
So there we have it. Let me leave you with the Bard from Minnesota. Bet you never knew how threatening a simple “hello” can sound.