largest (adj.)

c. 1200, of areas, "great in expanse," of persons, "bountiful, inclined to give or spend freely," from Old French large "broad, wide; generous, bounteous" (12c.), from Latin largus "abundant, copious, plentiful; bountiful, liberal in giving, generous" (source also of Spanish largo "long," Italian largo "wide"), a word of unknown origin.

The modern English meanings "extensive; big in overall size; great in number" emerged 14c. Adjective phrase larger-than-life first attested 1840 (bigger than life is from 1640s). Large-handed has meant both "grasping, greedy" (c. 1600) and "generous, liberal" (1620s); also "having large hands" (1896). Living large is a modern colloquial expression (1994 in African-American vernacular), but large in the sense of "prodigal, lavish" is from late 14c. and, of circumstances, "comfortable, easy" from 1738, and in more recent use Farmer and Henley ("Slang and Its Analogues") have it as "impressively, to excess" from 1852.

In mod.Eng., a general designation for considerable magnitude, used instead of great when it is not intended to convey the emotional implication now belonging to that word. [OED]

An older sense of "freedom from prison or restraining influence" is preserved in at large "at (one's) liberty, free from imprisonment or confinement free to move openly" (late 14c.). The phrase, with the meaning "free or at liberty in a general way (without particulars)" is from 1620s; specifically of electors from 1741, American English.