For some reason we have been trained to eliminate 100% of weeds. Gardeners don't seem happy if the garden isn't pristine weed-free. They spend back breaking hours pulling weeds, buy expensive special hoes to get the job done quicker, maybe even spend more bucks on a mechanized cultivator. While I understand the need to keep most weeds down in population, I don't see the sense in being fanatical about it. Harmless weeds can actually be beneficial, helping to retain moisture and more importantly, providing habitat for garden friendly insects.
Personally, I see weeds as a resource. I harvest the majority of weeds for compost material. Some I simply flip into the soil as biomaterial. Others I chop & drop for mulch. I leave some simply because I'm not going to kill myself trying to get every last one. And I swear that a low population of assorted weeds is actually beneficial. And the shallow rooted weed types don't seem to interfere much with most veggies anyway.
The only weed that I serious battle is the Bermuda grass. It is aggressive, spreading quickly and forming a dense mass of underground stolens. It definitely impacts the garden plants, out competing them for root space, sunlight, and water. Other than this, I simply just keep the weed population low so as not to adversely impact my crops.