I'll take a stab. Think of it in terms of lifetimes. A high cross section means a short life time because that means that the reaction has a high probability of happening. But to get a sharp (and therefore tall) resonance, you want a very long life time. So some of the terms are inverted. Resonances are sort of reversed from usual cross sections like that.
You should be aware that I answer questions like this in order to make myself think, not necessarily because I am a world expert.