Origin and history of well-fed

Old English fedan "nourish, give food to, sustain, foster" (transitive), from Proto-Germanic *fodjan (source also of Old Saxon fodjan, Old Frisian feda, Dutch voeden, Old High German fuotan, Old Norse foeða, Gothic fodjan "to feed"), from PIE root *pa- "to feed." Intransitive sense "take food, eat" is from late 14c. Meaning "to supply to as food" is from 1818.

Middle English wel, "in a satisfactory or pleasing manner; laudably, properly," used very broadly to indicate successful accomplishment of the action in the verb it accompanies; from Old English wel "abundantly, very, very much; indeed, to be sure; with good reason; nearly, for the most part."

This is from Proto-Germanic *wel- (source also of Old Saxon wela, Old Norse vel, Old Frisian wel, Dutch wel, Old High German wela, German wohl, Gothic waila "well"), which in Watkins is reconstructed to be from PIE root *wel- (2) "to wish, will" (source also of Sanskrit prati varam "at will," Old Church Slavonic vole "well," Welsh gwell "better," Latin velle "to wish, will," Old English willan "to wish;" see will (v.)).

It has come to be used as the adverb of good. From late 12c. as "in a state of good health, soundly." Also used in Old English as an interjection and an expression of surprise. By mid-12c. as a mere intensifier (may well be).

Expression might as well (do something, as not do it, or as do something else) is by late 14c., as is as well as "in addition to."