(なんじゃく) Use this only about people. Someone who is mentally or physically feeble. OLD
よわい The most broad word for weak. Use this about anything.   $$$
(かぼそい) A very specialized word which is usually used in only two cases:Use this about someone who looks starving, or a voice that is little more than a croak. In either case, the feeling is that I’m surprised you’re even able to walk / talk at all, and could collapse at any moment.   PPP
(すいじゃく) Usually used about people who are sick and cannot take care of themselves – can’t eat their own food, etc.   PPP
れる(かれる) Wither – used about plants only. Generally.
(おとろえる) To wither, wilt, deteriorate. Use about plants, animals, or people.   PPP
する(あっかする) To grow worse. (If you want to talk about a relationship deteriorating, you have to use this one.)
れる(すたれる) Decline – used about the popularity of trends or celebrities. But it’s not as bad as 滅びる, which is like, the empire has been totally destroyed and sacked by barbarians. If something is 廃れる、 there’s still a  certain amount of fans of it.