For me true weeds are plants like
Wild Mustard Garlic
Wild Mustard Garlic is a tricky plant because it produces seeds even as it flowers. When you attempt to pull a flowering plant the tiny sees pods explode, leaving you a fresh infestation. The small white flowers are pretty but unassuming and not of particular note in the garden. Definitely not worth trying to cultivate this one.
Crab Grass
Crab grass is a tiresome weed which often hides out in the lawn as well as in dry corners. If allowed to establish it will kill off your grass by simply taking over. It does not remain green, seeds quickly and generously and has no particularly useful qualities that I know of.
Thistles
Thistles vary from small, non prickly (Milk thistles) to small or huge and vicious (see above). They are very invasive with roots to Australia. they have variously pretty flowers, but in my view this is not sufficient reason to invite them over for a visit.
Bindweed.
With pretty flowers, Bindweed has an incredible root system which is very hard to get rid of. It invades via root, but it also wraps itself tightly around any plant it can get attached to and basically chokes it to death.
Chickweed
Chickweed is a ground hugging little plant that consumes space like Packman on a roll. Pushes other plants out of the way. Not useful.
Belladonna
The Belladona vine is a very invasive and tough-to-get-rid-of vine. Should be handled with gloves on since it is toxic. Belladonna is used in Homeopathic medicine, however that is really not a god reason to have it in your garden.
Creeping Charlie,
