Yo Cliff....
This would have been a great post in our
new gardening thread!
But I digress.....
It depends on the weed. Some weeds don't have much of a root system and some do. Then there are those (like nutgrass) that has underground rhizomes that make it even harder to get by hand.
I applaud your efforts to minimize use of conventional control products.
You know, I was in the business of selling them for 10 years so it's in my DNA to go that route. The key is when using a control product to use it the way it is intended and in those cases you are not doing any harm.
I use them on my property and you should see the flora and fauna that thrive on my property!
But there are limitations of what they will do and sometimes mechanical means are the way to go.
It's a real science so no way to go into as much detail here but when you do it a while, you'll learn what to do with what weed on what circumstance.
Not sure that I helped but feel free to post any questions and I'm happy to give my thoughts....