A bookish term, it is often found in serious up-market periodicals, mostly next to nouns such as power, ambition and pride. It is not complimentary. A person or group described as overweening may demonstrate presumptuousness, arrogance, conceit, self-importance or an excessively high opinion of themselves.
While I share the general European aversion to the overweening US firearms lobby, gun ownership has two compelling arguments on its side.
The Independent, 18 Dec. 2012.
The word comes from the older noun and verb overween. Both have now almost entirely vanished but were available to the writers of an earlier age. That included John Aubrey in the seventeenth century, who produced this concisely damning word portrait:
A better instance of a squeamish, disobligeing, slighting, insolent, proud fellow perhaps can’t be found than in Gwin, the Earle of Oxford’s Secretary. No reason satisfies him but he overweenes, and cutts some sower faces that would turn the milke in a fair ladie’s breast.
From the collection of essays, not published in his lifetime, that are now known as Aubrey’s Brief Lives.
Perhaps one reason why overween became unfashionable is that we lost its second part. Ween is Old English, a Germanic form that survives, for example, in modern German wähnen, to imagine or to believe wrongly. In English, it meant to think or surmise. By the nineteenth century it had ceased to be a common verb and turned up almost exclusively in the fixed phrase I ween:
Of legal knowledge I acquired such a grip
That they took me into the partnership.
And that junior partnership, I ween,
Was the only ship that I ever had seen.
HMS Pinafore, by W S Gilbert, 1878.