ichidan verb
languish; grow weak and feeble
Describes a gradual decline in strength or vitality, often due to illness, age, or hardship. Somewhat literary.
長い闘病の末、彼は次第に弱り衰えていった。
After a long illness, he gradually grew weak and feeble.
衰える is a more common and general word for 'to decline' or 'to weaken'. 弱り衰える emphasizes the process of becoming weak and languishing, and is more literary.
弱る means 'to weaken' or 'to be weakened', often physically or mentally. 弱り衰える combines this with 衰える to express a more prolonged and severe decline.
Compound of 弱り (continuative form of 弱る 'to weaken') + 衰える 'to decline'. The exact historical derivation is uncertain, but the combination intensifies the sense of progressive weakening.