This weekend = the currently occurring weekend or the weekend less than a week in the future (if said on a weekday)
Next weekend = the weekend immediately following this weekend
If you’re driving down the road in your brand new Lexus and I say “Hey, I think I’m going to throw up; pull over next chance you get…” do you pull over at the next chance you get to, or the one after that?
Next means… next. Not the one after.
I am aware that I am alone in this opinion.
One rule doesn’t always fit all uses of a word.
True, but it’s a little odd you can use the actual meaning of a word to describe that the very same word doesn’t mean the actual meaning that you’ve just used when asserting that it doesn’t 
“Next doesn’t mean the next one, but the one after next”
Next!
However, I could see a situation where a passenger asks/ tells a driver too late to take the exit which is right there, so s/he says, “OK, take the NEXT exit.”
In Ethilrist’s favor is the fact that in Medieval English, ‘next’ and ‘nearest’ were one & the same word. Ditto last/latest.
What complicates things re: the weekend question, is that our calendar was designed with Sunday as the first day of the week & Saturday the last, but European calendars and the airlines start the week on Monday, probably inspired by the invention of the word ‘weekend!’
How about months/ seasons. Some people have already started to call (Northern) Summer 2013 “last summer!” Well it is the latest summer compared to now. But a case could be made that June–Sep. 2013 is still THIS summer because it’s part of THIS year while “last summer” should mean “summer of LAST year (2012)”!
I would argue that it does mean ‘next’, within the conceptual framework it appears - there is an immediate weekend; “this weekend”, and there is the next one; “next weekend”.
Next doesn’t necessarily mean “next to here”.
I’m fairly sure I’ve heard ‘this’ and ‘next’ used in exactly that context - i.e. “turn left in a bit - not this one - next one”
You’re not alone. Next in line means next, not the one after. Next to you means next to you, not one more away. Next door neighbor, my next car…
Those who adhere to next weekend being 2 weekends away are not using the word next incorrectly. They are not arguing that next means the one after next. They are saying that it is the next weekend after this weekend. If you can’t see that, you’re being obtuse.
Sure, but your next door neighbour isn’t next to me, so clearly the word ‘next’ doesn’t strictly mean ‘immediately proximal to the speaker’.
For the people who still don’t see this, try the following thought experiment:
I’m assuming that on Saturday or Sunday, you’re happy using the expression ‘this weekend’ - and ‘next weekend’ means the following one.
When do you consider the weekend to start? (12 midnight on the Friday/Saturday boundary? 5PM on Friday?)
Whatever that boundary is, wind back half an hour from it (so 11:30PM on Friday if your boundary was midnight). At this point in time, how do you refer to the weekend that’s about to occur but has not yet started? Is it still ‘next weekend’?