Picture getting to know a couple people in town. Learning that one person likes red flowers, or has trouble gathering wood and you bring the flowers or wood a couple of times. The interaction should not be initiated by the character and you will have to see if whatever efforts you take will benefit something more meaningful.
You would be able to test if you have a connection by trying to hold her hand. If she rejects move on. If you succeed in the hand hold, you may be able to lead her in a walk to a garden and sit for conversations.
So now you have a relationship and someone that you 'care' about. Now Skyrim can test your relationship by causing that town to be attacked and see if you come to the aid. Or if you try to care for other individuals, the character may find out about it and ignore you, leave you, or try to take revenge on you or the third wheel. (poison/assasination etc) If you are away for too long, the character could lose interest.
Anyway, all this can be up to the player's choice on whether or not they want to be tied to a character. But I think it would add to the realistic fantasy of the game and add to morality decisions.