U should feel lucky that ur partner is not overly possessive. An over possessive partner is the type that can't let go. This is the overly jealous type that would call u time a day, suspect u to be cheating on them, won't let u have a life outside of this relationship fearing, u might find somebody better, in the end u will find it suffercating.
Buddhism once said this about love, which I think make lots of sense, it say that to love is human nature and to reject love, due to fear or any other reason, is unnature and is bad for u and can be harmful to u, but to love and not able to let go, is also bad for u and will be harmful also to those u love. So, the secret is allow ur self to love, but able to let go, when it is time to let go. I've seen some guys, married to very hot girls, usually men married to really hot women, 2 thing would happen, either A. they live a very long life or B. they live a very short life, those who live a short life, can't let go and as a result, are always fearful of all the other guys out there who are also sexually attracted to her, they become possessive, jealous, controlling and out right insane, sometime if it isn't because they are already in a relationship, chances are she can file a restraining order, for this sort of almost obsessive stalker like behavior, this fear, is bad for their health and they ended up living a short life, The other type, because they are able to let go, they can be a bit French about it, the good thing about the French, is that they really know how to let go, when a relationship run its course, although we might not agree with many aspect of French people's attitude towards marriage, this is one attitude, that is really worth for us to learn from, been able to let go, they are able to live in the present of the relationship, thus he is less likely to be jealous, possessive, due to fear of his wife or girl friend cheating on him, because if it really do happen, they are able to let go, so, for them, at most, just get a divorce or break up if it happen.
As for girls, a guy who is possessive is because he can't let go, because they can't let go, they are willing to go that extra length for this relationship, so, at first this relationship is sweet, but after a while, because, he can't let go, the relationship will become jealous, possessive, restraining and suffercating, A guy who can let go, are more lazy, as a boy friend, but they are not going to be restraining and suffercating that control ur every move, in the long run, a boy friend that can let go, is better then one that cannot let go.