Give space.

It's best to always give someone some space, especially in a relationship. Romantic relationship, family relationship or relationship between friends. You gotta know where the boundary is. If you care too much and that person feels uneasy, then you know it's a sign for you to move back a few steps. When someone feels that his/her personal space is invaded, he/she will move away from the you. When this happens, don't go asking why he/she feels that way. You'll make things worse.

Maybe he/she is someone who doesn't like being cared for too much.
Maybe he/she doesn't like the way you care.
Maybe the care he/she wants is not from you.