Chickweed does not survive winter. Their seeds do and those seeds can germinate after several years.
Thousands of seeds are dropped on the surface of the soil when a chickweed plant matures. The seeds survive winter and germinate when conditions allow.
With flowerbeds, removing a thin layer of soil from the top of the bed early in the spring can eliminate chickweed. If you follow this technique, chickweed will be mostly gone within a few seasons. Remove the plants that appear during the season and do not let them go to seed. Avoid turning flower beds as buried seeds from chickweed will germinate once they are near the surface even after several years.
Chickweeed in your lawn is difficult if not impossible to eliminate. For lawns, I recommend Later's Chickweed, Clover & Thistle Killer. When applied as the chickweed flowers, control can be achieved with a single application. This product, unlike many other herbicides, did not damage my lawn.
Dandelions have a single tap root that will not regenerate if cut below soil level.
This weed is the scourge of many lawns and flowerbeds. We are told to spray the plant with a herbicide or to dig it out. The easy way is to cut the root with a utility knife just below the surface of the soil. This takes very little effort and the plant lifts easily. The root will not regenerate.
When your lawn is well watered and healthy, dandelion seeds cannot start.
Watch your clippings.
For years I could not figure out how grass was starting in the flowerbeds. If your lawn mover sprays grass clippings onto the flower bed, some of the clippings and seeds will start. The cure was simple. Always mow along the edge so that clippings go toward the centre of your lawn.