If anyone is looking for someone who is anti-tilling, here I am
You probably have perfect soil under your weeds right now. Tall weeds soften soil and bring up nutrients from very deep in the soil. If you mow those weeds down and use them as green manure (also called mulch) now you can recapture those formerly deep nutrients at the surface.
I need to make a list of short reasons why not to till. I may as well start it now. I could write an essay on each of these reasons, but I'll spare us all the verbiage. I'm sure I have a few more reasons filed away somewhere but these come to mind immediately.
1. Tilling disintegrates the soil crumbs prepared by beneficial bacterial microbes and turns them to powdery dust.
2. Tilling kills the beneficial fungi that aerate the soil for you.
3. Tilling closes the soil's pores and holes formed by the fungi and worms.
4. Tilling promotes bacterial bloom that blows the carbon (dioxide) out of the soil.
5. Tilling scatters the stratified microbes all through the soil. Some microbes only can survive at the surface and some can only survive a few inches down.
6. Tilling exposes old weed seeds to the sun to germinate.
7. If Mother Nature wanted us to till, she would till herself. Instead of filling the Great Plains, veldts, steppes, and tundra with millions upon millions of plowing hogs, she filled it with grazing bovine, elk, deer, antelope, sheep, equine, and goats. These animals don't even "scratch it in." They walk on it.
7. Tilling is hard and requires expensive equipment (a personal note

).
So how are you supposed to soften your garden soil? By using compost or mulch on the surface of the soil. I don't lightly scratch it in. I gently place it on top of the soil surface and dampen it. By putting it on the surface you form a layer that will keep the soil temperature more constant and help slow the loss of moisture in the soil. When the soil is kept at one temp and moisture level, the beneficial microbes in the soil can really take off. Plus when it does rain, the rain will hit the mulch and not the soil. When rain hits something to slow it down before it hits the soil, mechanical erosion is lessened.
If you wanted to do something to intensify the soil softening effect, put down an organic fertilizer to feed the soil microbes before you mow down the weeds.
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A few more things about weeds: are you sure you have to eliminate them? Are they just ugly or are they sucking valuable moisture and nutrients from your crops? Or are they bringing up moisture and nutrients with their deep roots. Or are they capturing nitrogen from the air and delivering it to the soil (like clover and other "leguminous weeds")? Or are they conferring a sort of immunity to disease and pests to your garden? Or are they bringing in beneficial insects, birds, lizards, and toads to the garden? Or are they providing photosynthetic sugars to the beneficial soil microbes? Or are they providing a home for mychorhizal fungi? Or are they grabbing soil with their roots and slowing rain impact with their canopies so that hard rains are absorbed instead of washing soil away?
Some citrus producers are finding that leaving the nutgrass in their orchards does no harm; saves time, money, and labor to try and eradicate it; and keeps the soil intact during thunderstorms. Furthermore they are wondering about the damage to the trees from all the herbicide they've tried. All in all, just changing their mindset about nutgrass has greatly improved their bottom line and their stress factor.