Finite element based shape optimization is a classical approach for solving realistic problems, such as those encountered in industry. However, some difficulties may arise from the divide between the parametrization of the shape using Non-Uniform Rational B-Spline (NURBS) functions used in CAD tools and the finite element representation of the geometry using piecewise linear functions used in solvers. An alternate approach based on isogeometric analysis has been recently proposed for which the solver is also based on NURBS functions. In this framework, the locations of NURBS control points are usually considered as optimization variables whereas the corresponding control weights are frozen. However, this a priori choice of weights imposes a severe limitation of the shapes that could be found by the optimization algorithm. In this work, we present and experiment a shape optimization algorithm where the weights are taken as optimization variables in addition to control points.