Weird isn’t really the right description for this word, which means something criminal or villainous, though it is rather unusual and tends to be high-flown in its applications. When it started life, in the fourteenth century, it referred to a person of the lowest morals, one who was “guilty of or addicted to atrocious crimes; deeply criminal, extremely wicked”, as the Oxford English Dictionary comprehensively puts it.
In the following centuries, it spread its meaning more broadly, so that writers with an urge to pepper their prose with elevated terms can now also apply it to ideas and actions as well as individuals — recent writers have referred to “flagitious acts”, “flagitious leadership”, and “flagitious foibles and craven crimes”. But that usage is hardly new. The career of the entrepreneur William Hudson during the British railway mania of the 1840s was described at the time as “one vast aggregate of avaricious and flagitious jobbing for the accumulation of wealth”.
The word is from Latin flagitium, a shameful act, and can be traced back to flagrum, a whip. So it’s a close relative of flagellate, to whip or scourge. But, despite the similarity in form and sense, and the opinion of some older authorities, it’s not related to flagrant, something conspicuously offensive, which is from Latin flagrare, to burn.