Many formulae in the representation theory of Lie algebras involve sums of weights, the most celebrated being that of H. Weyl [Math. Z. 24 (1926) 377-395]. In this note we will derive some elementary, but very useful, formulae for summing subsets of-weights of a Lie algebra representation. We also give a selection of applications of these formulae. (C) 2002 Elsevier Science (USA). All rights reserved.