Any covering will kill any current top growth , grass , weeds etc , but it won't rid the ground of any grass , weed seeds that are in the soil waiting to germimate as soon as conditions are right . That will be about the same time as your veg seeds !
Different strokes for different folks .
But now is the time to do any work the weather will allow you to do .
A good compost heap , manure heap will be invaluable . As will any drainage if needed .
Be as ready as you can for spring sowing .
A tarp or black plastic does keep the rain off the ground , so you can just pull it back and get the ground dug when poss , and then cover again .
I personally prefer to clear the ground of grass and weeds as i prepare the ground . Then let the weed seeds germinate , remove them and let the next lot germinate also .
The ideal would be to keep allowing them to germinate till no more appear , about 5 or 6 times , then sow the veg and you get almost no weeds at all .