Weight vectors and weight multiplicities are defined in terms of group characters. The characters appropriate to all the unitary irreducible representations of the unitary, orthogonal and symplectic groups are expressed in terms of S-functions. The resulting explicit formulae for weight multiplicities are used to tabulate results by making use of the definition of S-function in terms of standard Young tableaux. The results obtained give, for the first time, the k dependence of the weight multiplicities of the groups U(k), O(2k+1), Sp(2k) and O(2k). There is no limitation on the size of k nor on the dimensions of the representations.