There are some very small vertebrate species. The dwarf chameleon is a very cute example. But why are vertebrates on that scale so uncommon compared to invertebrates such as arthropods? Warm blooded creatures have issues with their metabolism as they get tiny, but even cold blooded vertebrates seem to be lacking at this scale.
At first I assumed that maybe it had something to do with the amount of time that they have had to evolve. Land vertebrates have been around for a bit less time than land arthropods such as insects, so maybe insects just has more time to take advantage of the niches that come with being that tiny. Looking in the ocean, we can find more small species of fish, and some large invertebrates such as crabs and their relatives, large clams, etc which might support that idea.
I have no idea if this is true though. Are there any biological reasons for why tiny vertebrates, on the scale of a few cm in size, are so uncommon?