The issue isn't as definitive as you might think. Ultimately, it comes down to what interpretation of "next" you consider to be correct. For example, the American Heritage Dictionary (4th ed) defines 'next' simply as
Immediately following, as in time, order, or sequence
Following this definition, "next weekend" will always mean the weekend with the start date in closes proximity in time. If the phrase is used during a weekend, of course, you'd be referring to the weekend following the one you are currently experiencing.
However, the issue gets more complicated if you look to other definitions. The Oxford American Dictionary has a specific definition for 'next' when used in the context of time:
(of a day of the week) nearest (or the nearest but one) after the present : not this Wednesday, next Wednesday
Here, we're given the choice: it can either mean the weekend with the closest start date, or the following one (as specified by the parenthetical addition or the nearest but one).
This definition has come about mostly because of usage development. Many words and phrases in the english dictionary have meanings contrary to their technical definitions, and yet are still used commonly and considered valid. Thus, while technically "next" implies immediate sequence, it is used in other ways (which dictionaries like the OAD have accommodated for validity), so it's really a matter of personal preference. For example, it is unlikely that I will even use the phrase "next weekend" during the week, because some people might be confused as to what I am referring to. Instead, I will say "this weekend," unless it is currently the weekend, in which case I will say "next weekend."