To enfeeble is to make someone or something very weak or fragile. Your governor's budget cuts might enfeeble the state's public school system.
If an illness weakens you — makes you feel frail and shaky — it enfeebles you. Aging enfeebles us, and the lack of Vitamin D in the winter also enfeebles many people. You can also say that making it harder for people to vote enfeebles the democratic process. The verb enfeeble combines the prefix en-, "cause to be," with feeble, with its Latin root flebilis, "that is to be wept over."