[Mrs. Robinson]

Stones are not mulch. They do not improve the soil because they cannot break down and they "bake" your plants in the sun.
As time goes by, they sink into the soil/sand and with the blowing wind, dirt ends up filling in the crevices giving weeds more opportunity to grow.

Pine straw is not the only mulch you can use. Alternatives would be wood chips, cypress mulch etc. Do not even consider shredded rubber!
I would remove the stones, put down a thick layer of newspaper ( yes, newspaper!), and a thick layer of weed block on top of that and then the mulch.
The newspaper will kill any up-and-coming weeds (no sunlight) and when it breaks down, will add nutrients to the existing soil.

No matter what you do, you will always get an occasional weed, but they are easy to simply pull when first growing.
Good Luck with whatever you do!