Motivated by the theory of knots, Geck and Lambropoulou studied so-called Markov traces on the Iwahori-Hecke algebra H-n of type B-n. These traces depend on two parameters and are linear combinations of the irreducible characters of H-n, where the coefficients are called weights. Orellana determined the weights explicitly for certain special choices or the parameters. In this article, we derive from Orellana's result a formula for the weights in general. As an application, we obtain a new proof of Hoefsmit's formulas for the generic degrees of H-n. Finally, we present a conjectural formula for weights of Markov traces on Ariki-Koike algebras. (C) 2001 Academic Press.