We use the word paved, differently. I call the finish material of any surface prepared for walking or driving, paving. In other words, cinders could be a type of paving. they're just not asphalt or hard. They're "soft" paving.

I guess that weed paper doesn't really work then ...? Figures.

It depends on what part of the country you're in as far as what's available for paving (granular material-wise) but shopping locally resolves the question. Just don't get anything that is loose and doesn't pack. It must pack in order to be "walkable." (To pack it must include material sizes from fine to coarse grit ... but probably nothing larger than 3/4".)

Granular material (cinders, stones or whatever) will NOT stop weeds. It is only diligence that will bring weeds under control. The trouble with fabrics and papers is that soil accumulates on top and weeds start. Then their roots penetrate the barrier. The "fabric" itself is sometimes very difficult or impossible to remove. I consider it a total waste of effort except for certain fabrics for certain possible OTHER uses. I've used cardboard covered with mulch for pretty good results, but this solution is temporary, too. Some weeds can still penetrate the cardboard from below and eventually many will sprout from above. If you can't use chemical control, then you must resort to other methods (light starvation and hoeing, etc) that you can keep up with. Keeping ground free of weeds is kind of like raising a child. If you let kids get away with anything, they will forever continue. If you let them know it's not even possible, they give up and comply. If you allow any weeds to persist, there will be a never ending crop of them. If you commit to constant weed eradication and normal mulching for 2 years (only the first year is really bad) then they will dissipate to almost nothing. In commerce, chemical control is the standard as otherwise, weed control would be prohibitively expensive. In most cases that means Round-Up. However, even that's not a panacea.