Even with the edge stitches, it still tends to curl. It's nothing you're doing, it's just the nature of the stitch. You can knit this in all stockinette in the round as a tube. If you're not skilled enough to knit in the round yet, you can knit this as a straight piece and seam it along the length. If you look at store bought scarves, that's what many of them are. Long stockinette stitch tubes with fringe on the bottom.