Welcome to the forum! Glad you are here!
1/3 of an acre, or about 14,000 square feet. Think 140' x 100'. That's about 4 times as big as mine. Just trying to put it in persepctive for me.
What crops do you plan to grow? You approach different ones different ways. Things you transplant you can usually mulch and really cut back on the weeds. You have to invest the initial time to do the mulching, but to me it is well worth it.
I also mulch in between the rows, in the walking space, to keep weeds out of there. I'm not certified organic so this would probably not work for you, but I use things like the cardboard from cereal boxes (the chemicals in the paint probably rule this out for you), the heavy paper (without the layer of plastic) from paper chicken feed bags, or things like that in between rows, then put weathered wood chips, wheat straw the chickens have worked over, or dried grass trimmings on top of that to hold the other stuff in place. It works pretty well without the paper product underneath, but I find it keeps my bermuda grass down better and keeps the soil more evenly moist whenI use the paper products under the mulch.
Some things you grow from seeds can be mulched once they reach a certain size, cucumbers for example. You usually have to clean the weeds out of them once, maybe twice, before they are big enough to mulch.
Some things become self-mulching, potatoes for example. If you plant them close enough together, once they start to grow they pretty much crowd out the weeds. I clean the weeds out when I hill them up and by the time they are hilled up properly they provide a living green mulch. So for them, you mulch them by controlling the space of your planting and hope you don't have any that fail to sprout which gives weeds and grass an opening. Cabbage, broccoli and some other things will also self-mulch once they get to a certain size, but you have to watch the spacing. If you plant them too close together you can cut production. Too far apart and they don't self-mulch. It is trial and error for what works for you.
Other than mulching with dead organic mulch or with living green mulch, both in the row and in between the rows, I can't really think of much else other than time and a lot of weeding. Weeds do consume a huge amount of time. Hope this is your day job.
Again, welcome to the forum.