Weeds cause a lot of thoughtless reactions, provoking misplaced fixations about cleanliness.
What are weeds? they are colonising plants where soil has been disturbed. They are the first steps towards a balanced ecosystem.
They do not drive other species away but merely fill the gaps where other plants cannot be supported by the soil. They are a symptom not the cause of a problem.
Chickweed

Here are a few of their qualities:
-deep root pumps for leached nutrients.
-fiberise the soil, countering compaction.
-hold the soil from erosion.
-help bring water to the top soil.
-they absorb excess salt.
-rich compost material, probably the best source in the city.
-provide a diverse diet to animals in the pasture.

-can be used in companion planting or as a sacrificial crop.
-they aid organisms in the soil through exudation.

-show whether soil is poor, acidic, compacted or alkaline.
-they're great in salads, teas, pipes, medicines and bouquets.
 

The list shows their role as indicators and other uses.
(the latin names link to their pictures)

Bindweed, field
(convolvulus arvensis)
Hardpan or crusty surface with light sand texture. Helps corn
Bracken, Eastern
(Pteridium aquilinum)
Acidic or lime soil; low potassium; low phosphorus
Buttercup, creeping
(Ranunculus repens)
Wet, poorly drained clay soil, acidic
Buttercups
(Ranunculus spp.)
Tilled or cultivated soil, acidic
Campion, bladder
(silene cucubalus)
Neutral or alkaline pH
Chickweed
(stellaria media)
Tilled or cultivated soil with high fertility or humus unless weeds are pale and stunted, then fertility is low. Edible
Chicory
(Cichorium intybus)
Soil with heavy clay texture, tilled or cultivated with high fertility or humus unless weeds are pale and stunted, then fertility is low. Edible
Cinquefoil, silvery
(Potentilla argentea)
Dry soil, often with thin topsoil; acidic or low lime
Coltsfoot
(Tussilago farfara)
Heavy clay soil; waterlogged or poorly drained; alkaline(?) or low lime. Smokable
Daisy, oxeye
Waterlogged or poorly drained soil that has been neglected or uncultivated; acidic or low lime, with low fertility. Collects calcium.
Dandelion
(Taraxacum officinale)
Heavy clay soil; tilled or cultivated; acidic or low lime, especially on lawns
Edible, strawberries
Docks
(Rumex spp.)
Waterlogged or poorly drained soil; acidic or low lime Edible
Grass, quack
(Agropyron repens)
Hardpan or crusty surface
Hawkweeds
(Hieracium spp.)
Acidic or low lime soil
Henbane, black
(Hyoscyamus niger)
Neutral or alkaline pH
Horsetail, field
(Equisetum arvense)
Sandy light soil, acidic or low lime. Liquid manure, blight protection when boiled and sprayed onto leaves. Collects silicon.
Joe-Pye weed
(Eupatorium purpureum)
Wet or waterlogged soil
Knappweed
(Centaurea spp.)
Acidic or low lime soil with high potassium
Knotweed, japanese no sympathy for this one
Knotweed, prostrate
(Polygonum aviculare)
Tilled or cultivated soil; acidic or low lime
Lamb's quarter
(Chenopodium album)
Tilled or cultivated soil with high fertility or humus unless weeds are pale and stunted, then fertility is low
Edible, good with cucumber, melon
Lettuce, prickly
(Lactuca serriola)
Tilled or cultivated soil
Meadowsweet
(Spiraea latifolia)
Wet or waterlogged soil
Great in wine
Mosses
(Musci class)
Waterlogged or poorly drained soil; acidic or low lime
Mullein, common
(Verbascum thapsis)
Neglected uncultivated soil; acidic or low lime; low fertility
Mustard, white
(Brassica hirta)
Neutral or alkaline pH
Edible, grape
Mustards
(Brassica spp.)
Hardpan or crusty surface; dry, often with thin topsoil
Edible, leave beneath grape
Nettles
(Urtica dioica)
Tilled or cultivated soil; acidic or low lime Edible,liquid manure, herb oil improver, tomatoes
Pigweed, redroot
(Amaranthus retroflexus)
Tilled or cultivated soil with high fertility or humus unless weeds are pale or stunted, then fertility is low
Edible, hold erosion, all nightshades
Pineappleweed
(Matricaria matrcarioides)
Hardpan or crusty surface
Plantains
(Plantago spp.)
Heavy clay soil; waterlogged or poorly drained; tilled or cultivated; acidic or low lime, especially on lawns
Edible
Shepherd's purse
(Capsella bursa-pastoris)
Saline soil
Sorrel, garden
(Rumex acetosa)
Waterlogged or poorly drained soil; acidic or low lime
Edible
Sorrel, sheep
(Rumex acetosella)
Sandy, light soil; acidic or low lime
Sow-thistle, perennial
(Sonchus arvensis)
Wet soil; neutral or alkaline pH
Edible, great cucumber, melon
Thistle, Canada
(Cirsium arvense)
Heavy clay soil
Yarrow
(Achillea millefolium)
Low potassium
herb oil improver