Back on subject, the tad in “tad bit” is an intensifier, just as the little in “little bit” is. Intensifiers are one of the commonest usages in English, some of them so old that we no longer even think of the original as having been intensified. Indeed some have to be further intensified in order to convey the heightened meaning we wish from them.
A discussion of intensifiers can be found in the excellent The Unfolding of Language: An Evolutionary Tour of Mankind’s Greatest Invention, by Guy Deutscher.