I don't pull a weed unless i can name it. I've heard repeated stories of people who can't keep the re-seeding annual poppy, Papapaver somniflorum, in their garden. I give them seeds year after year. "The early foliage looks like a lettuce leaf," i say. "Oh," they often say. "I thought that was a weed."
It does take a while to learn your weeds, and you may notice that some weeds like particular spots in your garden. Sheep sorrel grows in 2 of my strip beds, but not in the parallel third one. Go figure.
Part of our mindfulness practice is becoming able to identify our emotions. Mad. Sad. Glad. and all the variations on those themes. Once you can name your emotions, you are not tossed on the sea of i-don't-know-what's-happening-but-it's-really-uncomfortable. A wave of emotion washes over you; you feel at sea for a minute or two; you remember to be mindful; you name the emotion. Oh, that's what it is. Chances are the body and mind will relax, at least a little bit.
Name your weeds. Pull them out. Give the flowers a chance to bloom.