"by inches, inch by inch," 1580s, from inch (n.1) + Middle English meal "fixed time, period of time, occasion" (see meal (n.1), and compare piecemeal).
Entries linking to inchmeal
inch n.1
"linear measure, one-twelfth of a foot," late Old English ynce, Middle English unche (current spelling c. 1300), from Latin uncia "a twelfth part," from unus "one" (from PIE root *oi-no- "one, unique"). An early Anglo-Saxon borrowing from Latin; not found in other Germanic languages. Transferred and figurative sense of "a very small amount, small quantity" is attested from mid-14c. As the unit of measure of rainfall from 1845. Sometimes misdivided in Middle English as a neynche. Every inch "in every respect" is from early 15c. For phrase give him an inch ... see ell.
meal n.1
late 12c., mēl, "an occasion of taking food, a feast, a supply of food taken at one time for relief of hunger," also (c. 1200) "an appointed time for eating;" from Old English mæl, Anglian mēl, "fixed time, occasion; a meal," from Proto-Germanic *mela- (source also of Old Frisian mel "time;" Middle Dutch mael, Dutch maal "time; meal;" Old Norse mal "measure, time, meal;" German Mal "time," Mahl "meal;" Gothic mel "time, hour"), from PIE *me-lo-, from root *me- (2) "to measure."
Original sense of "time" is preserved in English in piecemeal; compare Middle English poundmele "by pounds at a time; generously." Meals-on-wheels for a social service offering home delivery of food to persons unable to purchase or prepare their own is attested by 1952 (from 1947 as a mobile food delivery service without reference to social services). Meal ticket first attested 1865 in literal sense of "ticket of admission to a dining hall;" figurative sense of "source of income or livelihood" is from 1899.
piecemeal adv.
"by pieces, in pieces, piece by piece, bit by bit," c. 1300, pece-mele, from piece (n.1) + Middle English meal "fixed time, period of time, occasion," from Old English mælum "at a time," dative plural of mæl "appointed time, food served" (see meal (n.1)). The second element once was more common, as in Old English styccemælum "bit by bit." Compare gearmælum "year by year," and inchmeal.