Is the pea gravel supposed to be mulch? Or is it mixed into the soil?
Do you WANT the pea gravel to be mulch -- as in are you planning to add more? Pea gravel mulch looks pretty and usually keeps weeds that spread by roots from coming up but seeds seem to manage to sprout find in them and you do have to keep up with pulling up the upstarts.
Creeping weeds that spread by above-ground runners like vines, grass, or (in my case) clover WILL take root as well.
Now, MY favorite method for re-furbishing a garden bed is sheet mulching. But I'm not sure if this will work -- it might -- if you want to keep the pea gravel mulch. I guess I would adapt the method by cutting the weeds down, laying 4~5 layers of wet newspaper on top, making holes in paper layers to plant desired plants, then layering with another inch or so of fresh pea gravel (or another kind of decorative mulch) -- just enough to hide the papers and keep them from blowing around. The paper will smother the existing weeds and eventually break down. If the soil is poor and need to be amended, I would add 1~1-1/2" layer of rough compost BEFORE laying down the newspaper.