1540s, from Middle English weten, variant of witen (see wit (v.)).
Examples from the Web for weet
It wor a weet mornin but yet it wor a varry welcome change, for it made all feel nice an' fresh an' cooil.Seets I' Paris|John Hartley
They wur not paid for weet days at th' furst; an' they geet it into their yeds at Shorrock were to blame.
The Weet, so call'd because he cries always before Rain; he resembles nearest the Fire-tail.A New Voyage to Carolina|John Lawson
At last, th' Board sattle't that they mut be paid for weet and dry,—an' there's bin quietness sin'.
My een are bad; an' awm ill all o'er, an' it's wi' nought but gooin' weet o' my feet.