What do you use to cover vegetable garden over winter to kill weeds

you can use newspapers,cardboard,heavy plastic,landscape fabric or tarps.However the trap will have to be removed for the next season of planting

You really want to pull these weeds out now as the seeds will get in your soil, and just make more trouble for you next year. Easier to pull out the weed now, then 100 plants that grow form the seeds next year.

You didn't mention your location. Here in Montana weeds will not grow in the winter. The black plastic should certainly work anywhere though

I understand that clear plastic actually does a better job. You'd get light transmission that would sprout the weeds which would quickly get toasted by the heat transmission. Soon as frost takes the rest of my garden and grass mowing is done it is what I plan to do to claim a different part of the lawn for my garden.

you have your own answer - tarps, black plastic, weed fabric, garbage bags will all work fine

Black plastic and tarps will prevent weeds, definitely.

Heavy cardboard boxes, flattened. THOROUGHLY soak with water, top with compost, top that with kitchen garbage mixed with fallen leaves, top that with planting soil, and come spring you will have a grand planting area.

Cardboard covered with compost and leaves that sits frozen over the winter will not have distingreated enough yet when it thaws in the spring to be ready to use as new planting base. This is a set up requiring more than one year to see returns.