time of weakness; moment of vulnerability
Refers to a moment when one is physically or mentally weak, often used in proverbs or set phrases like 弱り目に祟り目 (misfortunes never come singly).
Misfortunes never come singly: I caught a cold and then lost my wallet.
He was taken advantage of in his moment of weakness and forced into a bad contract.
Compound of 弱り (continuative form of 弱る, 'to weaken') + 目 ('moment' or 'occasion'). The exact historical derivation is uncertain, but the word is conventionally associated with the idea of a vulnerable moment.