The argument, as I understand it, goes like this:
Position A ("Ordinary, hardworking people"): "We say 'on Saturday,' we say 'on Sunday,' 'on Sunday morning' etc, why oh why not 'On the weekend'?"
Position B ("Vested media interests"): "Weekend = week + end = at the end of the week = 'At the weekend' = Shut The Fuck Up."
The problem I have is that, well, imagine the week like in the shape of a ruler, with the days as different coloured bands along its length. Now I'm walking along the top edge of the ruler, Monday Tuesday etch, and I get to the end of Sunday and it's like a cliff top, my arms are windmilling, there's nowhere to go, if I even shift my body weight forward a millimetre I'll plunge into the void. That's the definition of the End, right? So when I hear someone say "I'm having a barbeque at the weekend," I'm like "Are you crazy?! There's no room, you'll fall off!"
Now, compare this to "I'm having a barbeque
on the weekend" - it's a whole different picture, isn't it? You've got two whole coloured bands to play with, you can spread out the rug, even throw a bit of frisbee if you make sure the kids don't go too near the edge.
Of course, all this is demanding a degree of logic in the language that just isn't there. Why is a "put down" just unpleasant if you're a person but fatal if you're a dog? Why do we "settle down" but "fire up"? Why not butter someone down? The linguist's answer is that there is no answer. Trying to find one will just add more silliness to an already dangerously silly world. You know that rule about splitting infinitives? That you shouldn't say "to boldly go" but "to go boldly"? The whole reason for that rule was that some smartarse grammarian noticed that in Greek and Latin the infinitive was one word (and hence couldn't be split), and, on the grounds that Greco-Roman civilisation was the fount of all things good and holy, proclaimed that in English infinitives like "to go" should also be treated as one word. That's the only reason. In reality, split infinitives have always existed in English and no great harm has come of it.
But that doesn't mean you're going to catch me saying "At the weekend."
