I put my weeds on pavers or a dry place so they die off. Then they get collected when dry to the burn pile. Anything going to seed is either on purpose (to be collected) or torn off so they don't end up in the soil. You sure seem to be enjoying all the gardening lately, I'm happy to see that.
It depends, small weeds in dry weather are left on the soil to dry out and return to whence they came, large weeds are removed to the compost. in wet weather all weeds are removed as they will just re root and carry on if I leave them.
we ourselves also die;
but one thing never dies
the fame of him who has earned it
I try to pull weeds before seed heads and place them on the soil to cover any bare soil created by pulling the weeds (preventing further weed seeds from germinating). If they have seed heads, they go to the chickens. Seeds = protein. Any that germinate in the chicken run are quickly decimated.
Adding more mulch in the form of pulled weeds to the garden promotes worms which promotes soil health.
Wind in Her Hair tosses bigger weeds over the fence and mows over them later. She leaves the tiny ones that she hoes right where they land and they dry out and get turned under at the end of the season.
We need weeds to populate our walkways in the garden. So I tear them out of the beds and throw them on the walkways. I always hope they will root.
My husband uses a John Deere Z655 down the main aisles and an electric mower between the beds. Keeps everything under control. But right now with the extensive and fast hard hitting rains we've had, the center aisle is kind of muddy because the weeds washed away. We only started the system a year ago. That's when we got the raised beds.
My weeds are mostly crabgrass. I keep after it daily. Rarely has it gone to seed. Therefore I make compost of it after leaving it on cardboard to die. At a previous garden I piled it at the end of the row. It turned quickly to compost. That does not work here.
I don't compost up here; I'm afraid the local bear population would find it too tempting. Where we lived previously, I composted and yes, some weeds were included.
When I'm weeding the garden where I live now, I normally just throw the weeds outside of the deer fencing. It's near the front woodlot but in a clearing, and if the weeds take off there...well that's less bare ground to worry about. Let's just say my yard is becoming "natural".
I learned the hard way years ago, make sure when you compost, that whatever you throw in, does not have any sort of disease. For those? I put in a "trash" bucket, and throw it in the trash can out front.