backward vs half-witted

backward and half-witted both are adjectives.

Word	Noun	Adjective	Verb	Adverb
backward	No	Yes	No	Yes
half-witted	No	Yes	No	No

As adjectives, backward and half-witted are synonyms defined as:

Other synonyms of backward include feebleminded, slow-witted.

backward (adjective)	half-witted (adjective)
directed or facing toward the back or rear	retarded in intellectual development
(used of temperament or behavior) marked by a retiring nature
retarded in intellectual development
having made less than normal progress

backward (adverb)	half-witted (adverb)
in a manner or order or direction the reverse of normal
in or to or toward a past time
at or to or toward the back or rear