This was actually going to be a comment, but I ran over the character limit. So here it is.
I must inquire as to your definition of "belong."
Does belonging to someone make you the express and exclusive possession of that person? That is, you are the subject of that person, and bound by his or her will? From this definition of belonging, one may infer two logical consequences with regard to freedom. The first possibility absolutely precludes any form of freedom--that is, any action you perform must come from the express will of your master, and you may do nothing which is not commanded by this master. This is surely not what you are referring to. The other poses an owner-pet dynamic. The pet is granted autonomy only as long as its behavior does not displease the owner, and the owner's will is (ideally) followed. Even then, the pet may still make demands, and it may sometimes persuade its owner to change his or her mind.
What if belonging merely denotes a relationship? You are my friend. I do not own you as I own a dog or a car. You are "mine" only insofar as your relationship to me is that of a friend. This relationship has little to no consequence in regards to your freedom.
What of investment? Can one invest in a friend as he can in a pet? I believe so. And clearly, the friend's freedom is not limited in this investment as the pet's freedom is. It is therefore possible to belong to many, and have many invest in you, without significant consequences to your freedom.
What of love? Would those that truly love you "give" you back to yourself? I assume that by this you mean to strip away any "belonging" that existed. Using this assumption, we may examine the possible senses of "belonging" that we have heretofore outlined. Since we have already established that you do not intend to talk about an absolute master of your actions, we need only to examine the owner-pet dynamic and the friend-friend dynamic.
If I truly loved my pet, would I relinquish its belonging to me? That is, would I release it to the wild? This cannot be the case, even if I know that the pet is self-sufficient. If I truly loved it, I would provide it the best possible care, and by releasing it I am creating that possibility that it may suffer in the quality of its lifestyle. If I truly loved it, I would only release it if doing so would cause the pet greater good than harm. It seems that it this dynamic, an owner who loves his pet must not necessarily "give it back to itself."
What if this pet was self-sufficient and satisfied prior to it falling into my possession, and did not gain a significantly better lifestyle thereafter? That is, if I tamed a fox, and did not provide it with morsels more delicious, a shelter more comfortable, than it had already been accustomed to. In this case, would I release the fox if I truly loved it? No; for in taming the fox I have accepted responsibility for taming the fox. I have made him mine as I have made me his. Once again, unless releasing him would do more good than harm, I see no reason that my love must compel me to do so.
If I truly loved a friend, would I strip away this relationship of belonging? Would I cease to call this person my friend? This also cannot be the case.
Therefore, it would seem that truly loving someone does not prompt giving that person back to himself, if doing so means to remove belonging.
What if giving someone back to himself entails simply granting him more autonomy, or freedom? But would a doting parent let a child wander onto the train tracks? Would a good friend let you gamble yourself into destitution and ruin? Once again, it has been demonstrated that to truly love someone does not mean you have to give him back to himself.
What if giving someone back to himself simply entails granting him freedom as long as he does not cause himself harm? That is, he may do whatever he wishes, to you or others, as long as he himself is not directly harmed. Would true love require you to grant this freedom? No; for to do so would be to deny self-love, and concern for others. You can truly love a friend and still stop him from bludgeoning your face incessantly with a hammer--for to love is not to utterly obey, just as to be loved is not to be utterly controlled. Therefore, it would seem that love entails respect for the other as much as respect for yourself, and understanding of the other as much as understand of yourself. It is therefore a complete fallacy to utter something akin to "If you love me, then you would let me do whatever I want." A truer sentiment would read "If you love me, and have no self-respect, and have no concern for others, and are oblivious to the harm I may cause to myself, then you would let me do whatever I want." I am not here to prescribe morality, but I believe that the most true proposition is merely this: "If you love me, you would respect and consider my opinion and weigh it against your own before acting." For to do any more or less would be to either deny self-love or to love for another.
Lastly, your final paragraph is a simple case of equivocation. It is true that one can never been completely happy or completely free. However, the pursuit of one does not entail the complete abandonment of the other. It is true that one must exercise freedom to perform actions to reach happiness, but this freedom does not need to be absolute or infinite. Happiness and freedom can each only be obtained in degrees, and it is a mistake to claim otherwise.