In the recent past, the visibility problem in vision-based control has been widely investigated. The proposed solutions generally have a common goal: to always keep the object in the camera's field of view during the visual servoing. Contrary to this solution, we propose a new approach based on the concept of allowing the changes of visibility in image features during the control task. To this aim, the camera invariant visual-servoing approach has been redefined in order to take into account the changes of visibility in image features. A new smooth task function using weighted features is presented, and a continuous control law is obtained starting from it by imposing its exponential decrease to zero. Furthermore, the local stability analysis of the invariant visual-servoing approach with weighted features is presented. Finally, this promising way of dealing with the visibility issue has been successfully tested with an eye-in-hand robotic system.