Posted: 13/04/2013 at 18:29
Many will have recently germinated from weed seeds in the soil because the sheeting has helped warm the soil up. Others will be perennial weeds like dandelion which start coming up at this time of the year. Because they will be unable to photosyntensize due to lack of light (I presume they are mostly white/yellow in colour?), they will die as long as you leave the sheeting in place. To kill all weeds using weed suppressing membrane, you may need to leave it in place for a whole season. As soon as you plant anything or turn the soil, dormant weed seeds will be brought to the surface though, so membrane is not a panacea. There's an old gardeners saying that goes "One year's seed is seven years weeds." which is effectively how long it takes of diligent weeding before an area is as weed free as it is possible to make it.
If you have plants ready to go in, I would suggest making slits in the sheet and planting through it for now. You could hide the sheet with bark chippings for the time being. Keep peeking under the sheet and when the ground is clear later in the year, remove the bark and cut the rest of the sheet up (so you don't damage anything you have planted) to remove it.