"bottom of anything considered as its support, foundation, pedestal," early 14c., from Old French bas "depth" (12c.), from Latin basis "foundation," from Greek basis "a stepping, a step, that on which one steps or stands, pedestal," from bainein "to go, walk, step," from PIE root *gwa- "to go, come."
The military sense "secure ground from which operations proceed" is from 1860. The chemical sense "compound substance which unites with an acid to form a salt" (1810) was introduced in French 1754 by French chemist Guillaume-François Rouelle (1703-1770). Sporting sense of "starting point" is from 1690s, also "destination of a runner" (1812). As a "safe" spot in a tag-like or ball game, suggested from mid-15c. (as the name of the game later called prisoner's base). Hence base-runner (1867), base-hit (1874), etc. Meaning "resources on which something draws for operation" (as in power-base, database, etc.) is by 1959.
Meaning "low on the social scale" is from late 15c.; that of "low in the moral scale" is first attested 1530s in English. Meaning "benefiting an inferior person or thing, unworthy" is from 1590s. Base metals (c. 1600) were worthless in contrast to noble or precious metals. Related: Basely.