I stand with those who say a weed is a plant that doesn't play well with others. As ecologists, we need to ask not what a plant is, but what it's doing in the ecosystem. If it's physically choking other plants (like bindweed), smothering them (like bermuda grass), crowding the root zone with durable, woody roots (like trumpet vine), or making people sick (like ragweed, poison ivy, etc.), that is a detriment if not an outright threat to our efforts to build a functioning ecosystem. If the same plant is not doing those things in your particular locale, then that's great. But please don't try to tell other gardeners in other locales that those plants aren't causing problems for them.
That said, I believe it was Ruth Stout who said, "A handful of weeds is a nuisance. A wheelbarrow full is a resource."