mid-15c., "bound or obliged by law," from Old French lier, liier "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 it is from an Anglo-French *liable, or from an unattested word in Old French or Medieval Latin. The general sense of "exposed to" (something undesirable) is attested by 1590s. The unetymological use for "likely" is attested by 1850.
"liable to be doubted," 1620s, from French dubitable, from Latin dubitabilis "doubtful," from dubitare "hesitate, doubt" (see doubt (v.)). Related: Dubitably.
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.