"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.
word-forming element meaning "lacking, cannot be, does not," from Old English -leas, from leas "free (from), devoid (of), false, feigned," from Proto-Germanic *lausaz (cognates: Dutch -loos, German -los "-less," Old Norse lauss "loose, free, vacant, dissolute," Middle Dutch los, German los "loose, free," Gothic laus "empty, vain"), from PIE root *leu- "to loosen, divide, cut apart." Related to loose and lease.