to make (a living) or support (existence) laboriously: They managed to eke out a living by farming a small piece of land.
b.
to supplement; add to; stretch: to eke out an income with odd jobs.
Origin: before 1000;Middle Englisheken,Old Englishēac(i)an (intransitive), derivative of ēaca (noun) increase; Middle Englishechen,Old Englishēcan, variant of īecan (transitive) < West Germanic*aukjan; both akin to Old Norseauka,Gothicaukan,Latinaugēre,Greekauxánein to increase, amplify
c.1200, north England and E. Midlands var. of echen from O.E. ecan, eacan, eacian "addition, reinforcement," probably from eaca "an increase," from P.Gmc. *aukan (cf. O.N. auka, O.Fris. aka, Goth. aukan), from PIE *aug- "to increase" (see augment). Now mainly in phrase to
eke out (1590s). It means "to make something go further or last longer;" you can eke out your income by taking a second job, but you can't eke out your miserable existence. Obsolete eke "also" (O.E. eac, Ger. auch) is probably related. Related: Eked; eking