Weights for compact connected Lie groups

Let $\mathrm{\ell }$ be a prime. If $\mathbf{G}$ is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from $\mathrm{\ell }$, and $\mathrm{\ell }$ is a good prime for $\mathbf{G}$, we show that the number of weights of the $\mathrm{\ell }$-fusion system of $\mathbf{G}$ is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of $\mathrm{\ell }$-stubborn subgroups in compact Lie groups.