The opposite is what you want. Weeding is the main process. What you don't want to see in the garden is pulled out by the roots. What is left is what you want, and some of what you want goes to seed if you let it.
I've noticed some of the corn field's of the Navajo in Northern AZ. They just put an odd shaped field in a wash, with maybe a berm around it to hold onto the monsoon water. Even with their ability to copy modern Iowa corn farmers, it's still very primitive.
The farmers in some of the Anasazi (sp?) settlements merely built some dikes to direct the water where they wanted in rather random shaped fields.
I'm sure you're right that weeding changed the genome by taking down plants that didn't immediately show promise. And selecting plants that required weeding to survive.