It's not the weeds you see that are the problem, it's the ones hiding in the dirt, waiting to grow.
|Weeds in Rye|
By Agronom (Own work)
[CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)],
via Wikimedia Commons
The "Soil Seed Bank", also called the Weed Seed Bank, is the agriculture term for the ungerminated seeds already in your soil, plus any tubers and rhizomes that can propagate the weeds. It's why your nice freshly tilled and raked garden erupts into weeds in a week or two.
It is possible to manipulate the Weed Seed Bank to keep the weeds from interfering with your crops. The linked article has a good explanation of how this can be done, and what decisions the farmer or gardener has to make.
Your control strategy will have to adapt to the kinds of weeds you have, so the first step is to identify what you have. Are they annuals or perennials? Do they spread underground? Can the regrow from a stem or not?
The super-secret trick for control of annual weeds is: Never let them go to seed. If all you can do for now is cut them short to keep them from flowering and setting seeds, do it. You'll appreciate it next year or maybe the year after.
Perennial weeds have a long-lived root system, and may die back in winter and resprout in the spring. The young ones can be killed if you pull them while they’re young, before they have big roots. Mature perennial weeds such as dandelions and some thistles can usually re-sprout from bits of root left in the ground. Either dig them out completely or repeatedly kill the leafy tops to exhaust the root and eventually kill the plant.
The super-secret trick for control of perennial weeds is: Don't let them regrow enough to refill the food supply in the roots. If you are using manual control methods, check for regrowth frequently and remove it promptly. Even if you use a root-killing herbicide like glyphosate you may have to repeat the application a few times.