How do you identify weeds, is there some process?
I ask as I have this weed (see image) that constantly returns all over my garden and my efforts to find it online have come to nothing.
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I really hope I'm wrong, but I've a horrible suspicion this might be Japanese Knotweed - image here http://treeheritage.co.uk/japanese-knotweed-garden/
If it's everywhere and it is that, I hope its nowhere near your house - it'll punch through into your rooms inside if it is, so if close to the house, I'm afraid you'll need to call in the professionals.
Have you ever left any of it to get taller and grow on? If you have, do you have a photo of it, or can you describe it?
As for identifying weeds, its not that easy on line, what you tend to get shown are images of ordinary flowers and plants which are regularly sold for gardens. Sometimes, if a weed is classed as a wildflower (and they often are) you can find them that way.
In contribution to your first question, a process for identifying weeds; for USA weeds, I have successfully used the "weed identifier" tool from the University of Wisconsin. You type in all the characteristics you know, and then the weed identifier comes back with photos of all the suspects that meet your "requirements". Browse through until you find it. Even though the weed doesn't have to be from Wisconsin, they only have location choices in the US, but some of these plants are a problem in many different parts of the world, so you might find your culprit there even if your problem is in UK. Also I imagine there are lots of similar websites to be found covering other places.
Good luck with your problem plant. I have to say, it looks deceptively "pretty" in your photo.