There is another paradox that I need to resolve:
The Berezin integration rules for Grassmann odd variables give the same result as differentiation:
If $f=x+\theta\psi$ is a superfunction, the integral
gives the same result as differentiation
How is this supposed to work in supersymmetry, where the Grassmann coordinates carry mass dimension -1/2? If I integrate, I expect a result to drop mass dimension by 1/2, whereas differentiation would lead to a gain. In the above example, I end up with the same object. What is its mass dimension?