You may have one or all of these things:

1) You had deep-rooted weeds which did not get killed by the weedkiller. You might have killed all the leaves, but they've recovered and are strong enough to get through your barriers. Did you grub out all roots? If no, then if you cut off the weed leaves the minute you see them, you will eventually weaken the plant. This will take a long time. I tried injecting Roundup in the roots of the worst weeds I have. It was a lot of work and they recovered within a few weeks.

2) Your barriers have deteriorated over time, they now have holes which you can't see as it was under the marble chips. Many tree seeds start out with thin roots that can fit through a pin hole and then tear your barrier.

3) The marble chip layer was not deep/heavy enough to keep weeds from sprouting from above or below. It should be 3 inches, I think.

4) Over time, dust and leaves form a layer on top of your barrier, in between the chips and weed seeds can use that as soil and germinate.

The bottom line is there are few effective solutions that require no weeding. Weeding before the weeds get deep roots is the best thing to do.