The correct spelling and pronunciation is Aerith (Air-ith), with the th. I prefer Aeris (it sounds much better than Aerith), but that's how it is. According to the writers, the name was chosen as a near anagram of the English word "Earth" (stated in Ultimania). Japanese has no kana for "th", so they Japanese use su. For example, death in kana is "Desu" when representing the English word, and Behemoth is Behiimosu (ベヒーモス).
The reason Aerith ends up in some places as Earith is because the kana uses e then a, but if you look at Japanese kana for Aerial, you see the sound is "aer" and not "ear". Kana is all about sound. The person who converted to "Earith" actually guessed right that the su was th, but Baskett did not.
Aerith
エ ア リ ス
E A RI SU
The problem with kana is that you often need the writers to tell you the spelling they desired (as you can see above there are numerous possibilities otherwise like Aerlith aerlis aeris aerith aerisu aelisu). They did do this with some of the names but Baskett obviously never got a copy of the Official Establishment File. In that, it lists Aerith, Leno and Yrena (as opposed to Aeris, Reno and Elena). Aerith is the only spelling they later corrected, probably because the writers thought this was one mistake too many. And, because we now know that the word was taken from the English word Earth (and the fact Ultimania explains the spelling) we know how it is supposed to look and sound.
Part of my problem with the retranslation project is that those not listed in OEF can also have other spellings and meanings. The main one I am not sure about is Seto. Seto セト (Seto) can be Set.. セト（Set）
https://en.wikipedia.org/wiki/Set_(mythology)
And there is absolutely no way to know unless a writer tells you what they meant. Converting to kana is simple. Converting back to the original word is sometimes impossible. Japanese use the same symbols to represent l and r, use the same symbol for th , su and s, to name some of the issues. Sound cannot accurately represent spellings. And so now you know why Aerith ended up Aeris and Earith.
Just to hammer home my point... take Reno. The kana is simple:
レノ
RE NO
But the name is actually Leno (assuming the OEF is correct lmao).. because レ can be Le or Re. Only a document telling the localiser what is intended can fix that. The reason Leno was used is likely because it means "pimp/seducer" in Latin, and contrasts to the meaning of "Rude" which is likely taken directly from the English word itself. Often in the translation project, meaning and mythology have had to be the guide that we use when deciding spellings, other times documentation by the writers, and failing that, no change is allowed.
LMFAO!!!