Weeds are a never ending issue in most gardens. Much as I detest using chemicals in my garden, I can suggest you use a spray weedkiller on them. Spray the weed’s leaves on a dry day and when no rain is forecast (the rain will wash the weedkiller away). A bright sunny day is best. Do not cut back the leaves beforehand as the weedkiller works by travelling down to the roots via the leaves. The weeds will die pretty quickly. Do not pull them up until they are completely brown and frazzled. Weedkiller is safe for pets once it has dried. Most weeds spread their seeds in the air, like dandelions, so you will always have weeds. There are other ways to kill weeds such as covering them in black plastic but it does take months to do and pretty unsightly. Of course you can dig them out by hand but they will reappear if any root has been left behind. Weeds are survivors of the plant world!

Pull them out whilst they are still small, before the tap root develops, otherwise it weed killer time.

As Sonia said they are the survivors, they only need a bit of water for the seed to germinate and they can grow anywhere.

To make life easier, remove the gravel to one side, lay a proper weed membrane like plantex, not mypex as this is for building work, you end up with lots of threads sticking out at the edges which looks worse than the weeds. Then cover over with the gravel again. Weeds will still grow as I said above, but they will be easier to remove as the roots will only be in the gravel.

I live in the country and wouldn't dream of using anything as toxic as weedkiller. Once it's in the foodchain i.e. birds eating insects poisoned with it, it's horrible to think about. I also have lots of weeds and will have to remove them individually. You could try a piece of cardboard weighted down with big stones or something heavy to kill them first, might take awhile. They are much easier to remove in hot dry weather. You can also spray them with a vinegar/water solution and although it's slow it will kill them eventually, and then pull them out. Good advice about the gravel membrane from the AGI.

That'll take 15 minutes max to dig/pull out. Or buy a weed burner

I now have a gardener due to my health issues and she does a much better job with removing the weeds by hand than even the weedkiller I suggested, so you could always get them to do a one off weed remover a couple of times a year?