Good point soil.
A weed is a plant out of place. IOW if its growing where you don't want it, its a weed. Take black nightshade, if its growing over in the next county its black nightshade, if its growing in my garden its a noxious weed.
I don't want it in my garden. For one thing, it competes with my chosen plants, for another it is susceptible to all the diseases that often inflict the nightshade family, i.e. potatoes, eggplant, tomatoes, tomatillos and peppers. It would be well with me if it stayed over in the next county.
This is an extreme example, but all of the weeds compete vigorously with your garden plants for water, sunshine and soil nutrients. For me it is best to pull them when small and just leave them on the soil for mulch. Believe me, your chosen plants will do much better if the weeds are killed.
Purslane is a pain in the toosh. You can't leave it for mulch, but must toss it in the garbage can. If left in the garden, pretty soon that is all you have growing. I will not tolerate it in my garden.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-