To avoid your blanket from blowing away while you're not on it consider sewing triangular pockets on each corner to hold rocks or other weights to keep the blanket steady.
Fabric crafting weblog Sew, Mama, Sew! offers directions on how to sew a patchwork picnic blanket, but the intriguing part is their method of sewing rock pockets. You can visit the source link below if you need to learn how to cut and sew the pockets onto your blanket.
I'd also recommend adding velcro closures to each pocket; that way if you're going to be in an area without small rocks to use you can store helpful picnic items such as salt and pepper shakers or corkscrews in the pockets to stabilise the blanket without adding unnecessary weight.
If you're sewing a picnic blanket you may also want to consider our previous tip on packing a shower curtain to keep your picnic blanket dry and sew a thick shower curtain as the underside of your blanket.