IPA: /ˌoʊvərˈziːləsli/
KK: /oʊvərˈziləsli/
In a way that shows too much enthusiasm or eagerness, often to the point of being excessive or inappropriate.
She overzealously promoted her new book, which made some people uncomfortable.
Overzealously → It is formed from "over-" (meaning excessively) and "zealous" (from Greek "zelos", meaning fervor or enthusiasm) and the suffix "-ly" (meaning in a manner). The word describes acting in an excessively enthusiastic manner.
Think of being 'excessive' ('over-') in your 'enthusiasm' ('zealous') — that's why overzealously means acting with too much enthusiasm.