Other forms: dignified, dignifying, dignifies
To dignify something is to give it more worth than it deserves. Treating a silly remark as though it were an argument.
That ironic sense is where the word actually lives, and almost always in the negative: I will not dignify that with a response. Saying it refuses the insult and answers it at the same time. The straightforward sense still exists, meaning to make something worthy of respect, as in a ceremony that dignifies the occasion. The adjective dignified describes calm and serious bearing, and dignity is the noun behind all of it.
To dignify is to make worthy. Late Latin dignificāre joins dignus, worthy, to facere, to make, which is exactly why dignifying something with an answer is a backhanded compliment.
Old French
dignifier
English, today
dignify
Built from
From Old French dignifier, from Late Latin dignificare, from dignus (“worthy”) + ficare (in comp.), facere (“to make”). See deign and fact.
Etymology from Wiktionary, CC BY-SA