IPA: /ˌoʊvərˈwiːnɪŋli/
KK: /oʊvərˈwinɪŋli/
In a way that shows excessive pride or confidence, often to the point of being arrogant.
He spoke overweeningly about his achievements, making others uncomfortable.
Overweeningly → It is formed from "over-" (meaning excessively) and "ween" (from Old English "wenian", meaning to think or suppose) and the suffix "-ingly" (indicating a manner of doing something). The word describes acting in an excessively presumptuous or arrogant manner, as if one thinks too highly of oneself.
Think of someone who thinks too highly of themselves ('over-') and is excessively 'thinking' ('ween') about their own importance — that's why they act overweeningly.