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). 

"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). 

1660s, "suited to or characteristic of old age," from French sénile (16c.), from Latin senilis "of old age," from senex (genitive senis) "old, old man" (from PIE root *sen- "old"). The meaning "infirm from age; pertaining to or proceeding from the weakness that usually attends old age" is attested by 1882; senile dementia is attested by 1851.