We propose new sets of degrees of freedom, called weights, for the interpolation of a differential k-form in Whitney finite elements of arbitrary polynomial degree on simplices. They have a clear physical interpretation as integrals of the k-form on k-chains. This allows to consider quite general distributions of the supports, that are k-subsimplices not necessarily uniform, in a way here defined. We exploit this flexibility to investigate distributions that minimize the growth of the generalized Lebesgue constant when the polynomial degree increases. Preliminary numerical results for the edge element case support the nonuniform choice, in agreement with the well-known nodal case. [Tables, figures and thus conclusions have been corrected in this new version]