This isn't weird or obsessive, just a natural tendency of the male sex. Consequently, anything that can be related to sex will be commented on. If you don't want him to do something, say so. Don't wait for him to do even more. That doesn't mean sex.
Love is about caring for each other and understanding each other.
You can be a girl's emotional support when she's feeling down, but you can also hurt her much more easily than you could a guy, physically, but also emotionally. Do things sometimes to show that you'll go out of your way for her send her flowers, call her. No lying on each other. That's up to each couple to decide. As a Christian there are no concrete definitions of what too far is, but you will know in your heart what is too far for you.