Well is seems like a universal problem, VEGGI GARDEN WEEDS. I am an amateur and don't grow anywhere near the amount that BP or others do here. So a couple of questions.
BP, what does the organic community do to supplement the soil without adding outside seeds each year? I assume you also don't add fertilizer or lime to be organic certified. I live in an area with terrible soil, Ga. red clay, and have actively tried for the past five years to add good stuff whenever I could get it. Of course that brought a new crop of seed each year. I do till year round when the garden is free.
MarkV
Mark,
Sometimes, I am too passionate about this.

I studied, in reading and in field interview and observation work for two or three years before beginning my organic venture. I grew up on a "truck farm" in the 50s and 60s. Massive undertaking. But given the age period, it was a free-for-all chemically. I continued to garden until moving onto our property last year, when I desired to go full blown again, but full organic. Step by step. It doesn't happen over night. Lots of stuff I used to know, I must now re-learn, because this is different. There is both a financial and a passion interest for me in these matters. Just adding leaves, grass clippings etc, without hot, hot, hot composting is a recipe for weed introduction. I did this last year and have paid for my mistake. One's compost pile material is made using local resources to the person. I have leaves, pine needles, wood chips and most importantly, chicken manure at my disposal. That's about all I have, and I have to make it work, as does every gardener. No two situations are the same.
Bottom line? There isn't a quick and simple formula. It is a complex mix of variables that is large part science and good part art. I find it most challenging and most rewarding in every way, financially, mentally and physically. I am genuinely concerned about Genetically Altered seeds for virtually the sole purpose of being able to use Round Up type chemicals from Monsanto and others. I find that very disconcerting. Another topic, another day.

I prefer the term "sustainable" to organic, as it better describes the goals in my mind.
Twelve Steps Toward Ecological Weed Management in Organic Vegetables - eXtension
This is another article on weed control management without resorting to just grabbing the chemicals, which over the long haul, will defeat your gardening by eventually, over time, destroying your sustainability. Pesticides are worse because they kill everything. If it kills bad bugs, it harms good ones too and enough of it, over time, is likely to harm us as well.
Lime is a natural product and perfectly acceptable and used with great gusto by organic farmers. I couldn't function without it. I'm small potatoes compared the big boys in Iowa, Kentucky and other places.