How do weeds grow?
How can you get the upper hand?
Most really troublesome weeds have developed extraordinarily efficient reproductive systems. Either they produce vast quantities of quick-to-germinate seeds (think: dandelions) or they produce vast root-systems whose rhizomes and root-buds give rise to new plants without seeds. The key to least-toxic weed control (PDF format), then, is to prevent them from either producing seeds or from feeding their roots and thus extending their root systems -- or both.
From dandelions to kudzu, it's those extensive root-systems that make perennial weeds difficult to yank and eradicate. Throughout the summer and fall, the foliage they sprouted in spring is feeding their roots, which store the energy produced through photosynthesis. When the foliage dies back in fall, the plant becomes dormant, and when spring comes, it uses the energy stored in its roots (together with the nutrients in the air and soil) to produce new foliage.
In spring, many weeds in your lawn put on a growth spurt, which means that much of their energy is invested in their leaves. If you deprive perennials of their foliage at this stage, you seriously deplete their energy resources, damaging them more than would a similar injury later in the season. The investment metaphor makes it easier to understand why some sources recommend going after bind-weed, for instance, only when shoots are six to twelve inches long, and only when it is actively growing. Tackling it when it is dormant is like cutting off a fingernail; it does not hurt the plant (or at least not much). Cutting it back in late spring, however, means you're hitting it when and where it hurts. At that point, the roots are somewhat depleted by the effort that went into producing foliage, but the foliage has not yet started replenishing the roots. Annuals are simply easier to pull in the spring, before they have had a chance to develop an extensive root system, and before soil has dried.
In fall, many seeds are already either germinating or in place to do so. Killing seeds at this point means you won't have to dig up the plants they'd produce in the spring. Furthermore, if you can make a dent in the perennial weed's root system in the fall, you're already impeding its ability to produce shoots in the spring, and it won't have a chance to repair itself before cold weather ends the growing season.
So how do weeds grow? each one grows differently so it is not an exactly answer that can be given.