I don’t get any on my veggie beds, apart from a few oregano due to composting oregano cuttings. The compost layer at the start of the year shouold suppress most weeds. It is possible your weeds are from seeds spread by birds pooping on the soil, in which case netting is the answer. I do get lots of weeds around my raspberries, as the birdies like to bounce around and dustbathe in that area.
Small weeds around plants are rare when the surface compost is hoed before planting, so it has grown most of its weeds already. And there are less when soil is no dig as well.
I have heard that covering them up with newspaper and mulch would help. Just cover the area with several layers of newspaper and then cover it up with enough mulch to make sure that they are fully covered.If the weeds attempt to push through then you could add in another layer of newspaper and more mulch.