Is it farther or further?
late 14c. (from c.1100 as a surname), "a worker in any sort of lead" (roofs, gutters, pipes), from Old French plomier "lead-smelter" (Modern French plombier) and directly from Latin plumbarius "worker in lead," noun use of adjective meaning "pertaining to lead," from plumbum "lead" (see plumb (n.)). Meaning focused 19c. on "workman who installs pipes and fittings" as lead water pipes became the principal concern of the trade. In U.S. Nixon administration (1969-74), the name of a special unit for investigation of "leaks" of government secrets.
"lead hung on a string to show the vertical line," early 14c., from Old French *plombe, plomee "sounding lead," and directly from Late Latin *plumba, originally plural of Latin plumbum "lead (the metal), lead ball; pipe; pencil," a word of unknown origin, related to Greek molybdos "lead" (dialectal bolimos) and perhaps from an extinct Mediterranean language, perhaps Iberian.
"perpendicular, vertical," mid-15c., from plumb (n.). The notion of "exact measurement" led to extended sense of "completely, downright" (1748), sometimes spelled plump, plum, or plunk.
To botch; ruin: I tho't I plumbered it (1930s+)
Completely; entirely; stone: What he said was plumb silly
[1748+; fr notions of exact extent and precision associated with the plumb bob or sailor's plumb line (for measuring depth of water), ultimately fr Latin plumbum, ''lead'']