  We present and analyze a discontinuous Petrov-Galerkin method with optimal
test functions for a reaction-dominated diffusion problem in two and three
space dimensions. We start with an ultra-weak formulation that comprises
parameters $\alpha$, $\beta$ to allow for general $\varepsilon$-dependent
weightings of three field variables ($\varepsilon$ being the small diffusion
parameter). Specific values of $\alpha$ and $\beta$ imply robustness of the
method, that is, a quasi-optimal error estimate with a constant that is
independent of $\varepsilon$. Moreover, these values lead to a norm for the
field variables that is known to be balanced in $\varepsilon$ for model
problems with typical boundary layers. Several numerical examples underline our
theoretical estimates and reveal stability of approximations even for very
small $\varepsilon$.
