thin, weak
羸 centers on a state of physical depletion: being thin, weak, or worn out. The two given meanings are closely related aspects of lacking strength or substance.
羸 is composed of 羊 (sheep) above a complex lower element that likely originated as a phonetic component. The exact historical development of the lower structure is uncertain, but the character is traditionally associated with the idea of a thin, weak sheep or emaciation.
A sheep (羊) sitting on top of a jumble of parts that looks like a worn-out body: imagine a scrawny, weak sheep that has become thin and tired.
For ルイ, picture a weak sheep named Louie who is so thin he can barely stand: Louie -> ルイ, and his frail body matches the kanji's meaning.