Showing my age I was going to suggest newspaper to suppress the weeds, but then I remembered that the internet/computers put a stake in the heart of that one. However, If you have a paper shredder, the shreds are great for that, too. You could also use thick plastic sheeting. The black kind warms the soil and suppresses the weeds. If you use plastic do not forget to poke some holes in the lower areas so the rain can seep into the soil.
