Ita doesn't really mean 'yes', the true meaning is closer to 'so/thus'. It's used as 'yes' by an implied 'est'.
French 'oui' comes from 'hoc ille', which basically means 'this' (think of how people on the Internet write '^ this' to express agreement).
Overall more common sí (also used in French) comes from Latin sic, which you see in English often after mistakes in an original text as a 'just like that/just so'. It had the same meaning in Latin, moving to just 'yes' in Medieval Latin.
I had this very same idea, but, on the contrary, "sic" means 'so/thus'
"Ita" is the affirmative adverb.
Very interesting, I already noticed some other, quite peculiar Slavic connections... like 'Quomodo te habes' being a word-for-word equivalent of 'Jak się masz' for 'How are you'. To my knowledge, no modern Romance language uses this particular structure, literally 'how do you have yourself'.
"Jak sie masz" has no link with a Latin root.
Slovak is a Slavic language, it's not possible that Latin got an influence on the Slovak grammar. But human languages have often common logics, they are the product of our brains, and we have the same ones. Several logics, but a finite number of logics.
I noticed these "word-for-word equivalents" many times while learning French (am a native Slovak speaker). Even if they are from different language families, this is the reason I always found Slovak and French to have much more in common than Slovak and English. It's truly amazing how sometimes you can see (at least I think so) the ancient common roots of such different languages.
Stergi is right for the "yes" meaning. I think you mean it means "yes", but your comparison with "no/not" is really confusing, and could show you think it means "no/not", rather than "yes".
The enclitic nē is absolutely not "no/not".
It's "no/not" only when you translate it in English.
Do you like cheese? You like cheese, don't you?
So, it's your own translation, but not the meaning in Latin.
The meaning is only to show that it's a yes/no question, there's no "not" or "no".
https://fr.wiktionary.org/wiki/nae#Latin (in French)
I translate this page:
From common Indo-European *h₂en-, giving ναί, naï in ancient and "ano" in Czech.
Adverb used to make a positive statement (yes),
It's often used with a pronoun : yes, sure, certainly, of course, in truth...
Tu nae, Plaute.
vulgar variant for nē .
https://www.prima-elementa.fr/Dico-n02.html (In Latin & French)
This word is an invariable part of speech
truly, indeed, verily, assuredly
nae, vulgar form for nē (v. 3. ne), particle of assurance, verily, truly
Yes, logeion says it's ranked under 50 times, but, on the other hand, they give the translation, and (many) other dictionaries do, so it's absolutely not an obscure word.