@Time Waster I do a lot of community garden plus I have a large garden myself.
My suggestion is to remove the stones, wash them, reuse them.
Do it in stages, make a barrier with a piece of wood or similar to isolate an area to work on.
The membrane underneath weed it as best as you can, then cover with a thick layer of cardboard, making sure to overlap it so that the weeds do not get light.
Then put the clean stones on top, add more stones if needed.
You need to wet the cardboard before adding the stones, or let it get rained on.
Lots of cardboard can be had for free from local shops, recycling skips or bins.
You will have to take any plastic labels/tape off them, only Amazon boxes are totally biodegradable, no need to take the tape off.
You can also buy rolls of cardboard or jute membrane, available from the usual retailers: much less faff but at a cost.
In 2020 I de-weeded a large area this way, but I used wood chips on top of the cardboard.
The first weeds started to emerge last year, no bad.
Weeds will always come back, self seeding
I had one of those compost bulk bags in the same place for a year, pots and other garden stuff on top.
Some weeds were happily growing through it!