mid-15c., "bound or obliged by law," probably from Anglo-French *liable, from Old French lier "to bind, tie up, fasten, tether; bind by obligation" (12c.), from Latin ligare "to bind, to tie" (from PIE root *leig- "to tie, bind"). With -able. Perhaps from an unattested word in Old French or Medieval Latin. General sense of "exposed to" (something undesirable) is from 1590s. Incorrect use for "likely" is attested by 1850.

Proto-Indo-European root meaning "to tie, bind." 

It forms all or part of: alloy; ally; colligate; deligate; furl; league (n.1) "alliance;" legato; liable; liaison; lien; lictor; ligand; ligament; ligate; ligation; ligature; oblige; rally (v.1) "bring together;" religion; rely.

It is the hypothetical source of/evidence for its existence is provided by: Latin ligare "to bind;" Albanian lidh "I bind," and possibly Middle Low German lik "band," Middle High German geleich "joint, limb."

late 15c., "burdensome," from charge (v.) + -able. Sense of "subject to a tax or payment" is from 1610s; that of "liable to be made an expense" is from 1640s; that of "liable to be charged" (with an offense, etc.) is from 1660s. Related: Chargeability.

"liable to be doubted," 1620s, from French dubitable, from Latin dubitabilis "doubtful," from dubitare "hesitate, doubt" (see doubt (v.)). Related: Dubitably.

"justly liable to objection, calling for disapproval," 1779, from objection + -able. Related: Objectionably.

1510s, "liable to sin, morally weak;" c. 1600, "liable to break;" a back-formation from fragility, or else from French fragile (Old French fragele, 14c.), from Latin fragilis "easily broken," from root of frangere "to break" (from PIE root *bhreg- "to break"). Transferred sense of "of frail constitution" (of persons) is from 1858.