It's nice to think that you can keep some of the nutrients accumulated by weeds in your garden. Many of the weeds are even 'hyper-accumulators', digging up minerals from deep in the soil with their long tap roots. But some of the same weeds are what may be termed 'pernicious' or 'noxious' you can sense the general feeling towards them by gardeners, can't you?
Why this loathing of such potentially helpful native plants aka weeds? It's because they won't die! If you put these in a compost heap so they can break down and return the goodness to your compost, they won't play ball. They don't volunteer to decompose, they grow.
A couple of methods of deprivation to weaken them and make them submit are to first drown them, dry them in hot sun, or put them in a black plastic bag for a lengthy stay.
Drowning starves the roots of oxygen, drying dehydrates them and the black bag deprives them of light so they can't make their own food (photosynthesize) and they starve to death. After a spell in solitary confinement they are safe (and dead) enough to go into the compost.
The death-bath (drowning) produces a liquid in which nutrients have been released and it makes a good liquid feed. It may also stink to high heaven! It is debatable how long the weeds need to be in water before they give up the ghost, the longer the better. Some weeds that are happy in temperate climates may even be able to survive the bath. Creeping buttercups for example, like to have their feet wet and aren't safe to enter your compost after a dunking. For these plants drying would be a better option but, hold on, they