late 12c., "lacking strength or vigor" (physical, moral, or intellectual), from Old French feble "weak, feeble" (12c., Modern French faible), a dissimilation of Latin flebilis "lamentable," literally "that is to be wept over," from flere "weep, cry, shed tears, lament" (from PIE *bhle- "to howl;" see bleat (v.)). The first -l- was lost in Old French. The noun meaning "feeble person" is recorded from mid-14c.
"act of taking food," Old English feding, verbal noun from feed (v.). Feeding frenzy is from 1989, metaphoric extension of a phrase that had been used of sharks since 1950s.
1893, American English, in the figurative sense "fear or doubt that reverses an intention to do something;" the presumed Italian original (avegh minga frecc i pee) is a Lombard proverb meaning "to have no money," but some of the earliest English usages refer to gamblers, so a connection is possible.