I was taught that, for a farmer, weeds are Nature's support crops and are vital to a healthy system. Now, there is a point in the beginning of our cash crop's life where we have to fight for its little life and take down the weeds, but once the cash crop is big enough to not be overpowered by the weeds, let them grow.
Weeds come in all shapes and sizes, both on top and root structure. Some weeds are vines to cover and protect the soil, some are tall and woody, some have thin and abundant roots, like grasses, and some have a single tap root, like a turnip. Each weed has its sole purpose, which is to grow, flower, and produce babies. The structural makeup of the plant will tell you the purpose. Like grasses are designed to hold soil in place with their many fine root hairs, and a tap rooted plant is designed to break up compacted soil. The thing that separates weeds from our garden plants is they grow much faster. They grow faster by design; their main purpose is to build soil. Some species of weeds, called pioneer species, not only grow fast, but they produce carbon quickly as well. This carbon, when they die, lasts a long time in the soil, helps build structure, and helps retain water. Weeds have certain nutrients that they absorb from the soil, bring to the top, and release when they die or compost.
So looking across an abandoned field you will see a variety of weeds growing, each of them is a reaction of whatever deficiency the soil has. Over time the field will eventually become a jungle, or whatever the geographic location dictates. For example, the taller weed that has a small daisy type flower growing in our area is known for drawing calcium out of the soil. So an abundance of this plant is an indicator that your soil is lacking calcium. I have encountered farmers that can look at a field and tell you what your soil needs just by looking at the weeds.