My hubby lets the grass grow tall in the yard. Then he collects it and uses it as mulch for our gardens. We have weeds all around us. The property next door is abandoned and there are tons of weedy things there. The grass mulches helps alot. If a weed does grow it's very easy to pull out.

It seems to me that a little bit of regular soil cultivation, even with a soil rake or a hand fork, would do the job. Wouldn't hurt the veggies you have growing either. Just dig 'em in (the weeds). You do that before the weed roots get deep, and they won't be competing with your veggies.

I also get big winds from the horse fields next door and don't like to go out during the winter and deal with windblown seed( I just pick the chard,kale,lettuce etc)
I plant 2 of my 8 beds for winter stuff and pile as many shredded leaves as I can, then cover with perforated cardboard so water can get through. Because most of the beds sink a bit, I usually add compost/soil about a month before planting in order to settle.
Cardboard usually lasts me 2 seasons. Nancy