Pull them. Then put down the plastic or a thick layer (3 inches or so) of organic mulch. The smaller weeds will not grow through the plastic or mulch. Larger weeds might make it through the mulch and gaps in the plastic. But, you can easily pull these. Weeding is a maintenance issue with a garden and, unless you’re willing to use sprays, pulling them by hand is the best way to do it.

I spent a few days with some relatives on their farm in Nebraska one summer and every day they went out to walk the beans for a couple hours. The whole family would walk between rows of the beans in their fields pulling the larger ones. Every couple weeks or so, they had to completely walk the beanfield to keep the weeds in check.

I have the same problem. Living in Florida, everything grows fast, especially the weeds. I’ve tried the expensive weed killers, boiling water, pulling by hand and drill bit, and the weeds still keep growing. Recently I tried salting an area, an old-timer recommended that method. I don’t know yet if it will work. If you want to, you can save this answer and email me in a few weeks for a progress report.

weeds should be pulled just before the sun goes down

The only organic way to kill weeds that I use is to weed the plants.
However, do not wait until the weeds grow.
Before you plant, go through the soil itself with your hands and get as much of any material that is not soil out of the soil. Do not use your weeds in your compost unless it is good stuff, like your herbs and things. On a lawn, for example, I put clover in - just a few plants - and now it is steadily helping me rid my lawn of the plantain weed that the Indians used to use for wild onions ! but which make it hard to mow.
Chick a weed - or little birdies on a branch weed is full of yummy seeds that a little bird likes, and so I let it grow in the beds at the edges. Whenever I find a weed I it is simply considered out of place and so I decide, should it go in the compost, or is it to be transplanted somewhere else. Then when your garden starts to grow, make sure you know what the baby plants are to look like, or you will pull all your garden out.
Another way I get rid of weeds is to put the unwanted ones like thistle in one part of the yard where I have built up the area there with dead plants. Or, put it in a plastic bag and take it away when you get rid of Spring or Fall clutter and debris. Weeds like Rhubarb leaves, Chaemycyparis [a yellow shrub] and herbal plants will just go back into my compost pile. So weeds come up?
Every weed is just a plant out of place. I wish people did not use
weed killer for Dandelions and Johnny jump ups, or Thistle, as our birds depend on these. There is a reason for weeds. We need to work with the Nature around us, and adapt our yard, and our garden to our use and needs.
Enjoy your garden.
bmtsjune Littlelady75

hi there weeds can be a pest i know have you looked at organic garden sites for help i have used fabric under my bark which as helped minimise the weeds hope this helps

Sounds like you have the basics. Try digging the worst of them up, preferably before they go to seed. Do all you can to keep them from flowering. Continue to mulch. A foot of mulch is good. Weeds may be a fact of life.