You have to get rid of the weeds before you can sow a cover crop. And tilling is not the answer - it will just redistribute roots and seeds throughout the garden and the problem will be worse next season.

Smothering them is your best (and least effortful) option. Cover the area with layers of cardboard or newspaper and then cover those with a thick (3-4 inches) layer of organic mulch or compost. By the time you are ready to plant next spring the weeds will have been smothered (dead), the cardboard/newspaper will have broken down and then you can till it and the mulch into the soil, rake to smooth and then plant.

If you use a mulch instead of compost, pick a non-woody mulch - leaves, straw, grass clippings, etc. Wood-based mulches will tie up nutrients if worked into the soil next season but that can be adjusted if necessary........just another step you don't need to take.

You will still need to stay on top of the weed situation next season. Weeds happen -- it's just hard to get around it. Again, the application of a thick mulch surrounding the plantings will help to keep weeds to a minimum.

I have a lot of maples and a couple oaks in my yard, so I bury my gardens under several inches of leaves in the fall. I typically do this on a dry day when it's supposed to rain in the evening or overnight so the rain tamps the leaves into place.
In seriously overweed areas, I've put down a layer of cardboard or old carpet to smother out the area too.

Great suggestions above.

And just to add, that if you till now you leave your soil open to winter erosion. That's one good thing your weeds will do for you as you leave them in place -- the roots will hold the soil in place, and when they are smothered, these same roots (now dead) will add to the organic matter in your soil.

So mulching is a win-win. And there is a possibility that your soil will be ready for planting in the spring by just raking aside the mulch -- that is, you might not have to till at all if you don't want to.

We are in a totally different climate than you but my aunt prepped her garden by covering her entire garden with a layer of leaves/grass clippings mix, tilling it all in and then adding another layer of leaves/grass clippings for the winter. Seemed to work pretty good.

Lloyd

A first year garden can be really "weedy", but keep in mind that most all of what w do refer to as "weeds", unwanted plant growth, are also wild flowers that can harbor beneficial insects, pollinators and predators.
You could till the area and till in those "weeds" adding them to the organic matter in the soil and seed a cover crop, some of which have allelopathic (growth suppressing)properties, or cover the area with a good mulch
(tree leaves are good here).
Have a good reliable soil test done as well, now, so any amendments necessary can be added now and be ready for use next growing season. Contact your counties office of the University of Maryland Cooperative Extension Service about that soil test. In addition you may want to use these simple soil tests to help guide you in making the soil into a good healthy soil.
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Here is a link that might be useful: UMD CES

The issue with winter mulch is providing homes for vermin.
Your mowing of the weeds is likely cover crop enough and the mulched up tops by the lawnmower is probably enough mulch.

You need to protect the soil from erosion but deep cover is not required.
I have gone with minimal cover for my garden because of the voles coming in and destroying my trees and bushes.

Since this is a veggie garden, I wouldn't worry about the voles over winter (if they are even an issue for you.) Any tilling you do will collapse tunnels next spring.

IME, many of my veggie garden weeds are either grass growing in from the edges or annual weeds. Neither of those will be helped by a winter mulch, but if you have lots of perennial weeds, the GG48's advice is absolutely the right thing to do. If you have annual weeds and a small garden, you could try covering it with clear poly sealed at the edges with board or burying the edges. It will allow the area under the plastic to warm up during the day when there isn't snow, but since it has no insulating value, it will get cold at night. Hopefully, that will encourage many of your annual weed seeds to germinate and then get frosted, cutting down on the viable seed bank.

More importantly, plan to use a seed-free mulch in the garden next summer. It will conserve moisture and cut down on weed germination (most weed seeds need light to germinate) as well as reduce disease from soil splashing onto plants during storms. Also, invest in a scuffle hoe AKA stirrup hoe . I have a large garden where I use two of these (on 9" and on 3") to remove any weeds in unmulched areas, and it rarely takes more than a half hour a week to keep things fairly weed-free. It cuts on the pull and push and need not be lifted, and so is less work.

Also, I don't know if your weeds have gone to seed, but preventing that in future years will help reduce the next year's weeds to some degree, though weed seeds have a long life in the soil, so it may take a while to see much reduction.