I've had a bait of it

Wondering about the derivation of "I've had a bate of it." Recently heard in N. Carolina. The usage was to indicate the person had had enough of something.

I've heard that and thought it would be easy to find in one of my southern dictionaries. No luck yet.

Found it under "bait."

bait n. -- food, generally a large amount (I eat a bait of black eyed peas and hog jowls New Year's.) From Southern Mountain Speech by Cratis D. Williams (Berea College Press, Ky., 1992)

bait -- n. a full meal. "I et me a bait o' ramps, and tasted them for a week atterwards." Also S. Car. "I et me a bait" literally means a mere snack, but jocosely it may admit a hearty meal... From "Smoky Mountain Voices: A Lexicon of Southern Appalachian Speech Based on the Research of Horace Kephart," edited by Harold J. Farwell Jr., and J. Karl Nicholas (University Press of Kentucky, Lexington, Ky., 1993).

(In W.Va., we said, "I ate a bite." Meaning a snack.)

Did "bait" in this sense come from "bite"? --rb

I am wondering if there is a connection.

Merriam-Webster:

Main Entry: 2bait
Function: noun
Etymology: Middle English, from Old Norse beit pasturage & beita food; akin to Old English bItan to bite