懦弱 describes a deeply ingrained personality trait — chronic timidity. For situational fear, use 害怕 (hàipà, scared) or 胆小 (dǎnxiǎo, timid). 懦弱 is harsher and more judgmental.
memory
Both characters share the 'heart' radical (忄/心), because cowardice is a matter of the heart. 懦 = weak-hearted, 弱 = weak.