In permaculture, weeds are not necessarily the enemy. In fact, many weeds have beneficial qualities that make them a valuable addition to your understory. Before you destroy all those weeds, educate yourself on why they are worth keeping.
Dandelion (Taraxacum officinale) is often the bane of those who wish for perfect lawns, but in permaculture, they are one of the most prized plants. Dandelions accumulate potassium, silicon, potassium, magnesium, calcium, iron, and copper, making their edible parts extremely nutritious and also medicinal. When they die, all those nutrients are returned to the soil. Their deep tap roots break into and loosen hard soils of all types, including hard-pan clay. The flowers attract beneficial insects such as ladybugs, parasitoid wasps, lacewings and bees. The flowers can also be made into a tasty wine. Dandelions seed prolifically, as anyone who has ever blown the seeds off the stalk and watched them fly knows. This is wonderful if you have a field of hard or depleted soil you're trying to rehab.
Chickweed (Stellaria media) is a very pretty little cool-weather weed that loves disturbed, infertile soil. It shows up in early spring, attracting pollinators looking for nectar. This dainty little weed spreads like wildfire, and is an excellent accumulator of phosphorus and potassium, which are returned to the soil when it dies, is turned under or used as chop-and-drop material. The greens are delicious raw in salads, and domesticated birds, fowl and rabbits treat it like candy, while it gives them much needed nutrients. As a groundcover, it is best left to die and decompose on its own with its roots intact to return the nutrients to the soil and add organic matter as they decompose.
Lamb's quarters (Chenopodium album), also called goosefoot, is a weed with centuries of historical use as a food and permaculture plant. It often grows in old over-fertilized fields, and can improve poor soil over time. Lamb's quarters accumulates manganese, nitrogen, calcium, phosphorus, and potassium, and since it grows taller than some weeds, it can be cut back frequently for chop-and-drop. Its leaves are so tasty, however, you will likely want to remove the smaller ones first to cook as a very nutritious potherb. Since they produce so many seeds, they can become invasive, but it is one of the better plants for rejuvenating soil. As an added benefit, local chefs often pay high prices for the leaves, so you may use it for a source of income. Tell a landscape designer, like one from Weiler's Lawn & Landscape, about the beneficial weeds you'd like to use in your permaculture garden. Even in urban yards, you can find a place for these plants to grow with abandon and provide nutrition for your garden and your body.