Those rails are really small, thus really light. They didn't look so unsturdy as in swaying side to side, they just slid on top of the grass. You can bury the legs, or buy some stakes and stake them into the ground. You can either get the big U shaped ones and put them over the legs or get a long, heavy duty one, drill a hole through each leg, and put them through that hole. If they are swaying side to side you need to brace it like this.
(paint ftw) The braces are in red, I've done this with my rail and it fixed all of my issues. However, you might not want to brace like this on the last set of legs because you hit them when you spin off the rail. There's different ways to brace and I could explain another way if you don't want to go about that route. I could also take a picture of my rail tomorrow to help explain what I'm talking about if you want.