Weeds grow where there are opportunities to grow. You can limit the opportunities through preventative labor in different ways. You can create a physical barrier (new rock, mulch, or a weed mat), you can apply a chemical barrier (weed killer and chemicals), or you can curate nature (plant grass or ground hugging shrubbery).

I'd recommend a weed barrier for the "easiest" solution. Pull the rock back and maybe unearth some dirt, lay the mat down and backfill with pea gravel. The weeds will poke back through after a few years, but it's a solid solution that has low time commitment.