  A weight ring in type A is the coordinate ring of the GIT quotient of the
variety of flags in $\C^n$ modulo a twisted action of the maximal torus in
$\SL(n,\C)$. We show that any weight ring in type A is generated by elements of
degree strictly less than the Krull dimension, which is at worst $O(n^2)$. On
the other hand, we show that the associated semigroup of Gelfand--Tsetlin
patterns can have an essential generator of degree exponential in $n$.
