late 14c., "weak, unsound" (of things), from Latin infirmus "weak, frail, feeble, not strong or firm" (figuratively "superstitious, pusillanimous, inconstant"), from in- "not, opposite of" (see in- (1)) + firmus "strong; stable," figuratively "constant, trusty" (from suffixed form of PIE root *dher- "to hold firmly, support" ). Of persons, "not strong, unhealthy," first recorded c. 1600. As a noun from 1711.

late 14c., infirmite, "disease, sickness; lack of capability, weakness," from Old French infirmité, enfermete "illness, sickness, disease; moral weakness," and directly from Latin infirmitatem (nominative infirmitas) "want of strength, weakness, feebleness," also "the weaker sex" [Lewis], noun of quality from infirmus "weak, frail" (see infirm). 

Proto-Indo-European root meaning "to hold firmly, support." 

It forms all or part of: affirm; confirm; Darius; dharma; farm; fermata; firm (adj.); firm (n.); firmament; furl; infirm; infirmary; terra firma; throne.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit dharmah "custom, statute, law," dharayati "holds;" Prakrit dharaṇa "a holding firm;" Iranian dāra‑ "holding;" Greek thronos "seat;" Latin firmus "strong, steadfast, enduring, stable;" Lithuanian diržnas "strong;" Welsh dir "hard," Breton dir "steel."

"left-handedness," 1890, from Italian mancinissmo, from mancino "infirm (in the hand)," from manco, from Latin mancus "maimed, infirm, crippled; lame-handed," from PIE *man-ko- "maimed in the hand," from PIE root *man- (2) "hand."

"state of being broken down by infirmities," c. 1600, from French décrépitude (14c.), from Latin decrepitus "very old, infirm," from de "down" (see de-) + *crepitus, past participle of crepare "to crack, break" (see raven).

"tending to render weak or infirm," 1680s, with -ive + Latin debilitat-, stem of debilis "lame, disabled, crippled," figuratively "weak, helpless," from de "from, away" (see de-) + -bilis "strength," from PIE root *bel-"strong" (see Bolshevik).