If I put 許 into a Japanese dictionary I get either the results "gari" or "kyo" for it alone, which don't seem to be words on there own but there is a meaning explained. Jisho says the kanji means permit or approve, which seems to be more in line with kyo words.
Anywho, it is used for the "baka" part in bakari, bakarini and bakaridenaku. I've noticed so far in Japanese that a lot of parts of words combine to make new words (sometimes of another word class entirely). Plenty of times the combination seems to make sense. And I wonder if the same goes here. What does bakari mean at its core if it has one and why does combining it with these other things result in these new meanings?