How do I destroy this weed on the balcony?!

I don't know if you can pull out the root. I recently tried the method myself, but haven't pulled on the brown plants yet. Something keeps coming up. But if it's dead, doesn't it then not matter? The main thing is that it doesn't grow back.

The water has just been prepared

It is a balcony, and there will also be some kind of foil under the stones, right? Do you think I can't damage anything with the boiling hot water?

I don't want to cause any harm to the ugly woodlice there either... but using chemicals isn't any nicer than using hot water, right?

a kind of foil

Now it's really time for a photo!

Buy glyphosate on Ebay (pure, not a mixed product!). Spray diluted with water over the plants, wait a week, and done. Removes all plants reliably and also kills the roots - nothing will grow there anymore.

And yes, I know it's not the best for nature - but it helps. And it lasts permanently.

So, I had poured several buckets of boiling hot water over the stuff. This weed is now brown, partially somewhat shriveled, but I still can't get it out with the roots. I think we probably have to lift the slabs a bit and somehow scrape everything out, and then I'll pour something chemical in. This is really annoying.

So you didn't have to pour it bucketfuls to achieve this result

Now just pluck out the brown remains and leave it at that. The roots should be dead by now, nothing will happen anymore.