Witham is the name of several villages in Lincolnshire and Essex. With a pun on wit, the expression little, or small, Witham was used proverbially for a place of which the inhabitants were remarkable for stupidity. For example, the following, from A fourth hundred of epygrams (1560) by the English playwright and epigrammatist John Heywood (circa 1496-circa 1578), ridicules the extravagancies of fashion in the 16th century:

Whence certaine thinges came first.

Whens come great breeches? from little wittam.
Whens come great ruffes? from small brain forth they cam.
Whens come these round verdingales? from square thrift.
Whens come these deepe copped hattes? from shallow shift.
Whens come broudered gardes? from the towne of euell.
Whens come vncombe staryng heades? from the deuill.
Whens come these vntrimed scarfes? from folly, John.
Whens come these glitteryne spanges? from much wanton.
Whens come perfumde gloues? from curiositee.
Whens come fine trapt moyles? from superfluitee.
Whens come corne crooked toes? from short shapen shoone.
Whens come wylde hie lookers? from midsomer moone.
Whens come fayre painted faces? from painters tooles.
Whens come all these? from the vicar of saint fooles.

Used as a common noun, the name denoted a witless person, as in this passage from The anatomie of absurditie contayning a breefe confutation of the slender imputed prayses to feminine perfection, with a short description of the seuerall practises of youth, and sundry follies of our licentious times. No lesse pleasant to be read, then profitable to be remembred, especially of those, who liue more licentiously, or addicted to a more nyce stoycall austeritie (1589), by the English pamphleteer Thomas Nashe (died circa 1601):

He that wil seeke for a Pearle, must first learne to know it when he sees it, least he neglect it when hee findes it, or make a nought worth péeble his Iewell: and they that couet to picke more precious knowledge out of Poets amorous Elegies, must haue a discerning knowledge, before they can aspire to the perfectiō of their desired knowledge, least the obtaining of trifles be the repentant end of their trauell.
Who so snatcheth vp follies too gréedilie, making an occupation of recreation, and delight his day labour, may happes proue a wittome whiles he fisheth for finer witte, and a Foole while hée findes himselfe laughing pastime at other mens follies, not vnlike to him who drinking Wine immoderatly, besides that hee many times swallowes downe dregs, at length prooues starke drunke.

According to Henry Harrison in Surnames of the United Kingdom: A Concise Etymological Dictionary (1918), Witham is from Old English witan hām, wita’s home or estate, wita meaning wise man, councillor.