1540s, from Middle English weten, variant of witen (see wit (v.)).
Online Etymology Dictionary, © 2010 Douglas Harper
Examples from the Web for weet
E'ening grey and a morning red, put on your hat or ye'll weet your head.The Proverbs of Scotland
When the chaffinch says "weet, weet," it is an infallible sign of rain.Poachers and Poaching
So Mike for all he was weet to the skin, set off to look for Amos.More Tales of the Ridings
It's no a fit nicht for ye to be oot at a', mair by token 'at ye're no the ablest to stan' cauld an' weet.'Robert Falconer
“You maun be weet, laddie,” said the old master of the boat, helping me out of her with the aid of two of the other men.Will Weatherhelm