This work provides a general framework for the weighted piecewise vector-valued rational interpolation. When the interpolation function on each piece is at least $C^N$-continuous, by selecting a proper weight function, the interpolation function obtained from the weighted piecewise interpolation method can also be $C^N$-continuous on the entire interval. Then, by applying the weighted piecewise vector-valued rational interpolation framework to several common vector-valued rational interpolation algorithms including Thiele method, Side method and Fitzpatrick method, a series of weighted piecewise vector-valued rational interpolation methods can be achieved. Some numerical experiments show that, the utilization of the weighted piecewise interpolation method can achieve better approximation effects meanwhile reduce computing time.