E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A Yorkshire way-bit. A large overplus. Ask a Yorkshireman the distance of any place, and he will reply so many miles and a way-bit (wee-bit); but the way-bit will prove a frightful length to the traveller who imagines it means only a little bit over. The High-landers say, A mile and a bittock, which means about two miles.