It is thought that the name "weasel" comes from the Anglo-Saxon root "weatsop" meaning "a vicious bloodthirsty animal".
A weasel word (also, anonymous authority) is an informal term for words and phrases aimed at creating an impression that something specific and meaningful has been said, when in fact only a vague or ambiguous claim has been communicated.
Regardless of whether weasels in fact suck eggs, a belief that they do implies an egg shell devoid of its contents. Thus, words or claims that turn out to be empty upon analysis are known as "weasel words". The expression first appeared in Stewart Chaplin's short story "Stained Glass Political Platform" (published in 1900 in The Century Magazine), in which they were referred to as "words that suck the life out of the words next to them, just as a weasel sucks the egg and leaves the shell". Theodore Roosevelt attributed the term to Dave Sewall, claiming that Sewall used the term in a private conversation in 1879. Winston Churchill wrote: "The reserve of modern assertions is sometimes pushed to extremes, in which the fear of being contradicted leads the writer to strip himself of almost all sense and meaning."
Additionally, the definition of the word 'weasel' includes: n. a sneaky, untrustworthy, or insincere person; v. to manipulate shiftily.  A weasel word (or phrase) can quite likely be understood to come from a position of intending to manipulate the communication, in a sneaky or underhanded manner.
In the political sphere, this type of language is used to "spin" or alter the public's perception of an issue. In 1916, Theodore Roosevelt argued that "one of our defects as a nation is a tendency to use ...'weasel words'; when one 'weasel word' is used ... after another there is nothing left".[11
I am certain there is much more that can be added but I'll leave that to those that follow...