I recently read a post on Facebook encouraging gardeners to grow purslane in their gardens because it can be eaten. BAD IDEA!! Purslane is a weed that will take over your garden. A weed can be any plant that grows uncontrollably.
I currently have horsetail in my garden, a terribly hard weed to get rid of that spreads by roots and spores. I was silly enough to read and believe all of its wonderful benefits as a natural, healing herb. Ha Ha Ha Ha. It will be many years until I've freed my soil from its benefits.
Do yourself a huge favor. Kill weeds when they are small. Hoe often. Don't let weeds go to seed. Some weeds spread by their roots/tubers so don't think that rototilling will help because it only spreads them. If you do dig up weeds dispose of them away from your garden. A lot of times I put mine in buckets until they rot away.
Be careful if a plant starts spreading like a weed because it could be your next gardening nightmare - I'm thinking parsley right now.
If you do have persistant weeds that you're are fighting take heart. You're in good company. Be persistant and you will get rid of them. Keep a song in your heart - Gardeners don't let your weeds to grow up to have babies - sung to the tune of
"Mammas Don't Let Your Babies Grow Up to be Cowboys" by Waylon and Willie.
https://www.youtube.com/watch?v=RePtDvh4Yq4