If I say “this weekend”, I might be referring to the one just past, or the one just coming. Usually you’ll be able to tell from the context, especially the tense of the surrounding sentence. But it’s inherently ambiguous.
Now, if I say “last weekend”, the ambiguity thickens. If I were to say, for example, “I went to Abergavenny last weekend”, apart from this being a lie, you’d be unsure which weekend I was referring to. Your interpretation might be swayed by the day on which I made the assertion: if today were Monday the 16th, you might suppose I was referring to Saturday and Sunday the 7th and 8th *; but if I said it on Friday the 20th, I might easily be talking about the 14th and 15th. (It’d still be a lie, but that’s not the point.)
“Next weekend” is even worse, because it’s about the future, and any inherent uncertainty could result in missed appointments, communication breakdowns, acrimony and tears. The same ground rules as for “last” probably help; but they don’t cover Wednesday. “I’ll see you in Abergavenny next weekend”, spoken over the phone even on a Thursday, could have repercussions way beyond the “oh well…”. Wellington texts Napoleon: “Wen U sed CU nxt wkend, Waterloo, I thought ment…” ** You get the picture.
So far, I don’t remember this amphibology placing me in any life-changing situations, maybe because if it’s that important, I’ll probably be specific about the actual dates. I’ll be in Abergavenny on the 20th. (That’s a lie too, by the way.) Mainly, I just wanted to type the words ‘Abergavenny’ and ‘amphibology’, and see those dinky little superscripts popping up on the dates.
* A calendar might be helpful at this point
**Thanks to Bee for that one.