The one weed that comes to mind right after hearing "I have to go weed the garden" is this one. It is everywhere. And it is always there. Even after you think you pulled all th little and big ones. It is still there. That's how cool is it!
Galinsoga parviflora
There is a reason why it is called a quickweed. One of the first that pop from the ground in early spring and one od the lasts that will die after the winter finally comes and freezes everything around.
It is native to South America but it took over the world like a real champ. It can be found in both Americas, Africa, Europe, Asia, Australia...
It grows like a mess reaching maybe 50 cm, though som stems can be longer. They bend and tangle with each other.
Small thin leaves and tiny little daisy like flowers are edible and can be used in soups and salads. Now when you think of how fast is grows and how little care (none) it deeds that is a lot of free food :D
Blooming time - all year round as soon as the stems mature. And they do really grow in the speed of light.
There is another one called Galinsoga quadriradiata that looks almost the same and is equally weedy.
It is impossible to get rid of completely unless you have some always hungry animals like chickens or goats that will eat whatever sprouts). It just a never-ending battle to remove what you an so it doesn't suffocate the veggies you actually planted and want to grow.
As a young girl I was feeling bad for it when it was blooming so nicely and my mum was piking it out. So I was taking the ones with roots and was planting them back in my own little garden (I had like a square meter of garden for myself an I could do what I wanted. So I was planting weeds!).
Here is a nice diagram from 1796 by Jacob Sturm.
source
Shot with Nikon D5500 + Sigma 105mm lens
All photos and text are my own.