Answer: The answer really depends upon how long the weed barrier has been in place and whether or not it has holes in it for air exchange and water penetration. If it is black plastic sheeting, I'd remove it in the fall and spread a 5-6" layer of organic matter (such as compost, shredded leaves, etc.) over the entire bed with the plan to till or dig the material into the soil just prior to planting. A 5-6" layer will shade out any weed seeds that might be lurking on the soil surface. Black plastic should effectively kill weeds and weed seeds if it has been in place for 3-4 months of hot summer weather, but you never know... You'll want to remove it this fall so the soil can breathe and drink up moisture from fall rains. If it's covered with organic matter, it shouldn't sprout weeds, but you'll have much healthier soil in the spring.
If you have air and water permeable weed barrier, leave it in place until a few weeks before you're ready to plant in the spring. At that time remove the weed barrier and spread a 2-3" layer of organic material over the entire bed, rototilling or digging it in to a depth of about 8". Then plant your veggie garden.
Best wishes with your veggie garden!
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