the word obsessed is a key warning some thing is wrong. concerned is fine, obsession is not
Well, I'm not sure that you could actually call Rider "obsessed" with Sakura. It's not like she spends every waking moment thinking about her, or is incapable of having feelings that don't relate to her. She just cares very deeply for her, and is willing to do whatever it takes to protect her.
I'd say Rider is more like a very protective big sister, really. She cares a lot for Sakura and will do whatever she must to protect her, but she's not "obsessed" in the sense you claim. In particular, in HA she doesn't just follow Sakura around all the time or anything, she does have her own interests.