during, on, at the weekend

I use on and during interchangeably. I have never heard at the weekend, maybe because I'm not British.

I'm in the US, for your reference.

Being british, 'at the weekend' is used most of all... I've never used during or on...

I say on the weekend in your example. I might say during for another excursion as in I will try to go hiking during the weekend. No real distinction, maybe. (U.S.)

"on the weekend" is also the Canadian usage

Generally in AE they are interchangable, but I'd agree with what I think k is saying, that there's a very slight impression to "during" of a sweep of time, than "on" which is a bit more of a point in time, rather than a sweep. If you usually do a bunch of things during the weekend, and you didn't have a fixed time during the weekend for doing something, but just fit it in, you might be a bit more inclined to use "during the weekend". "On the weekend" I think implies it's a bit more of a major part of your weekend. In the former case you might also say "I usually go shopping sometime during the weekend."

On the other hand, "Saturday" is a bit more specific timewise than "the weekend", so you'd be more likely to say "I usually go shopping on Saturday" whether it was your major Sat. exercise or just something you worked in at the last minute. I doubt even the Brits would say, "I usually go shopping at Saturday", tho it's hard to tell with them, since they don't talk the language good like we does here in the States.