Why is diabase/dolerite erosion resistant?
Diabase is indeed relatively erosion resistant. One of the reasons is grain size.

Consider the two other chemical equivalent of diabase: gabbro (coarse-grained) and basalt (glassy and fine-grained), which should potentially be similarly erosion resistant. This is not the case. Both gabbro and basalt erode very easily.

Coarse-grained rocks, in general, erode easily. The large grain size means it is relatively easy to dislodge individual grains out of the rock. You don't need a lot of water, for instance, to percolate between the not-many grain boundaries and release them. To make it worse, gabbros are full of minerals that are easily erodable such as plagioclase and olivine.

On the other hand, basalts also tend to weather easily. Having cooled fast, they are usually glassy which tends to crack during cooling. Glass is general is less resistant to chemical alteration than minerals, under similar conditions. Basalts also contain gas bubbles, which cause weakness spots in which the rock can break, leading to preferred weathering.

Diabase is fine grained, and contains no glass. It does not suffer from these two conditions. It is composed of very fine interlocking crystals that are very hard to dislodge, and is not penetrable by fluids.

That said, remember that it is all relative. A diabase will still weather faster than even the worst type of granite.