run down vs weary

run down is not an adjective while weary is an adjective.

Word	Noun	Adjective	Verb	Adverb
run down	No	No	Yes	No
weary	No	Yes	Yes	No

As verbs, weary is a hypernym of run down; that is, weary is a word with a broader meaning than run down:

Other hypernyms of run down include fatigue, jade, pall, tire.

run down (adjective)	weary (adjective)
	physically and mentally fatigued

run down (verb)	weary (verb)
use up all one's strength and energy and stop working	exhaust or get tired through overuse or great strain or stress
injure or kill by knocking (someone or something) down and passing over the body, as with a vehicle	lose interest or become bored with something or somebody
pursue until captured
move downward
examine hastily
deplete
trace