to a fault vs overly

to a fault and overly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
to a fault	No	No	No	Yes
overly	No	No	No	Yes

As adverbs, to a fault and overly are synonyms defined as:

Other synonyms of to a fault include excessively, too.

to a fault (adverb)	overly (adverb)
to a degree exceeding normal or proper limits	to a degree exceeding normal or proper limits