Do you think I have a partial tear instead of a complete tear if my knee is only weak on one side?

Not really. Weakness to one side does not sound as much like an acl injury. It sounds more like an mcl or lcl injury depending on which side it is buckling on. The acl is more involved in a rotational pivoting restraint than a buckling one. A partial acl tear should really feel like a normal acl except a touch looser. It should not be weak on one side or the other.