Obssession is just desire become addiction.
Love requires strong emotional bond, but it's main aspect is a point of consciously made commitment to love someone. This commitment is not feeling based, it is more like a promise that you will to make and to keep. You decide to love someone because you want to. Ideally the commitment is near unshakeable regardless of your emotional wild rides and contingencies of life. This is different from romance, which only remains so long as feeling and desire persists.
To obssess over something or someone is not to love them, it's to simply have an irrationally strong desire for them. Were it not for the desire, you wouldn't care, whereas with love how you feel does not matter, in the long run you choose to care.