Weeding

Weeds are good.

You should harvest them regularly and often to feed your compost heap.

Some weeds,  like docks,  cow parsley and mallow,  have very deep tap roots which penetrate the ground much deeper than your carrots or broad beans.   These roots collect water & minerals (plant food) and bring them up to the weed leaves.   By harvesting these leaves you transfer those minerals to your compost heap and bind them into humus.   When that humus goes into your vegetable patch it holds water and releases the minerals to your vegetables.   Don't bother to dig it under:  the worms will do that for you.   At the same time they'll create tubes and channels for water and air.

If,  while harvesting your weed leaves,  you didn't pull up the roots,  that's good in two ways.   First,  you didn't damage the vegetable roots which,  inevitably,  are intertwined with the weed roots.   Second,  you'll get another crop of weed leaves to harvest in a week or so!

Eventually,  the constant harvesting of its leaves will weaken the weed and the root will come out.   That's OK:  you've loosened the soil and you won't need to dig that bit!   You've created a long,  deep hole into which your plant roots can grow easily,  that worms can move in readily and which will carry water and air deep into the soil.

Other weeds are annuals.   They have shallow roots  which pull up easily,  and they make good compost.

Now that you can see no weeds,  sharpen your hoe (Yes: give it an edge like a kitchen knife!) and slide it through the top inch or so (no deeper!) of soil every couple of days.

And the compost heap?

Find an empty patch of vegetable bed and dump your harvested weeds there.   They'll cover the soil and prevent it drying out.   As they wilt their fluids will seep into the soil and feed the soil microbes.   They'll exclude light from the soil and so,  to an extent,  suppress the growth of more weeds.   The bottom layers will moulder,  and the fungi will convert cellulose and lignin into smaller,  humic,  molecules;  micro-beasts will come up to eat the fungi and then leave their dung in the soil.   The worms will leave casts under the weed heap,  and they'll 'dig' the soil for you.

When you want to sow seeds into that patch of ground,  simply move the heap elsewhere,  and sow the seeds.