Learn English – “Sent” vs “sent off” vs “sent out”

Although the phrase can mean that, and often does, it's also sometimes applied in a more broad context. To be "swept off your feet" is to be surprised, enthralled, exhilarated. Critics can be swept off their feet by an epic film; operagoers can be swept off their feet by a beautiful aria, etc.

As for how sweeping became associated with love, that's referring to the aspect of sweeping that means a smooth movement, not the act of using a broom. Ballroom dancers can sweep across the dance floor, a powdery snow can sweep across the barren fields. It's that smooth, fluid motion – and the idea of your emotions being carried in that fashion – that brought about the idiom. A strong ocean or river current can literally sweep you off your feet, and young lovers can do the same thing to each other, figuratively and emotionally.

In the sense ‘administer (punishment)’, I am quite certain that I have never used or even seen ‘mete’ on its own without ‘out’. It is to me an unbreakuppable (unupbreakable? Erm … inseparable!) phrasal verb construction, and leaving out the phrasal adverb is quite simply not possible in my idiolect.

As a copy editor and proofreader, if I had come across a sentence like your example from 2008, I would simply have assumed it was an error and added the ‘out’ back in—or possibly, if the context did not make the phrase clearer than it is in your quote here, I would have added a big, fat question mark, asking the author whether it is supposed to mean that the queen would measure the punishment (in whatever way that might make sense) and suggest that he recast the sentence entirely to avoid this ambiguity and jarring unidiomaticness.

However, this is all just my own, personal experience and gut feeling speaking.

Googling “mete punishment” in quotes does yield nearly 4,500 hits, of which at least some on the very first page appear to be (presumably) native speakers using the phrase without the adverb in this sense, in places where literacy and style would be expected (presumably):

The following sentence is from a December 1893 edition of Race and Place Newspapers (Richmond, VA):

Rape should be punished with death. The law decrees it, and we so agree. We insist that the law be left free to mete punishment and that the necessary safeguards be thrown around the accused to the end that the execution of an innocent man and the escape of the guilty brute may not be within the realms of a reasonable possibility.

Then there is this open letter from the Memphis, TN, Commercial Appeal, entitled Mete punishment where it belongs.

There are also some articles from the Huffington Post, etc.

So clearly, the adverb is not necessary to all native speakers. I do not know whether it is a coincidence that both the examples mentioned above are from the eastern/southeastern part of the US, or if there is indeed a dialectal difference here, with the phrasal verb being more loosely attached to the verb in that general area.

Googling “mete out punishment” in quotes yields over 700,000 results, which shows (even discounting incidental and disqualifiable hits) that the version with the adverb is far more common than without it, by a ratio of about 150:1 on the Internet as a whole. Presumably, this discrepancy is even greater in formal writing.

So I would strongly advise any writer to err on the side of convention here and always include the adverb. At least that (as far as I know) is not unidiomatic or ungrammatical to anyone.