Nowadays, being fast and precise are key requirements in Robotics. This work introduces a novel methodology to tune the stiffness of Cable-Driven Parallel Robots (CDPRs) while simultaneously addressing the tension distribution problem. In particular, the approach relies on the Analytic-Centre method. Indeed, weighting the barrier functions makes natural the stiffness adaptation. The intrinsic ability to adjust the stiffness during the execution of the task enables the CDPRs to effectively meet above-mentioned requirements. The capabilities of the method are demonstrated through simulations by comparing it with the existing approach.