Are those unwanted plants growing in the rocks and stones? That may be because over time dust and organic matter have collected in the spaces between them and provided a growing medium. In that instance there is nothing that you could put down that would stop them and the solution to this unwanted growth is to clean out the accumulated growing medium, the dust and organic matter that is there.

No, I stuck a few succulents and a blue rush plant in there. I just set this up a couple of weeks ago. The problem is some grass blades have been popping up. I may also have a problem in the future because there is a bird feeder to the right of the birdbath (above the large paver), and I imagine that any seeds that the birds don't get will germinate once organic matter does accumulate.

Depending on which grass species you have towels may be no more effective than a fabric "weed" barrier.

How deep does the edging go? How much of the grass was removed before the stone was laid down?

The area is surrounded with St. Augustine. It's pretty thin right now due to the cooler weather, shorter days, and shade. As we get into spring, it will get more sun light and heat, and thicken up. When I put down the rocks and pavers, it was pretty bare. I think the grasses and weeds that are emerging are from birdseed that was in the soil. The edging is only a couple of inches deep.

I've been looking around the internet, and I see that I'm not the first person to think of using towels. Sheets and blankets were also recommended as an alternative to plastic weed cloth. I'm going just give it a try in the next day or so. I have way to many old worn towels in the garage, and nothing to loose but a little time. BTW, I did find some smaller rolls of weed cloth at Home Depot of only $10, but the towels are free :-)

It was pretty bare and I didn't dig anything up. Probably a case of "there is never time to do it right, but there's always time to do it over". At any rate, I redid it this morning using towels as a barrier, so I think it will be OK for some time now.

I am wondering about the wicking action of the towels and how they might keep the soil surface wetter than ideal. But as long as you keep the towels away from the plant crowns, I think it should work. I would have tried it if I thought of it! Especially since it is not an area where you want to feed the soil. As was already said, things will grow on top of the towels, but that will happen with any barrier. Black oil sunflower seeds attract many types of birds and their seedlings are easy to pick out. The shells are messy so some use the shelled seed which of course is more expensive.

I used an old sheet under my compost pile to keep out tree roots and it was still intact at least a year later.