In modern mathematics here are not really infinitely small numbers. Analysis was carefully reformulated to remove them. There are models that involve ideal elements, but that is not really the same thing.
Your ordinary mathematician no longer uses infinitesimals, or even literal infinities, they use formalisms that involve limit processes, instead. For instance, something is true at infinity, in modern analysis, if whenever it is true of everything larger than a given size. The phrase 'is true at infinity' is just translated into that notion of an unbounded sliding scale and done away with as a genuine concept.
But even among those who do use them, the notions of infinitely small and infinitely large are not complete on their own. Of the infinitely large, there is more than one size, and the most relevant one of those sizes comes in several varieties. Of the infinitely small, there are also several varieties that all act differently.
So the question has every answer you might want. If your infinitely small bricks are point-sized, and you have countably many of them, your wall is definitely "of measure zero". If you have uncountably many of them, it can be any size you want, and you can keep pulling walls the same size at it out of it infinitely many times without making it any smaller or less dense. (This is the Banach-Tarski Paradox.) So we generally avoid collections of things that are point-sized, other than points, because that makes no sense.
But if they are infinitesimal (from a Nonstandard continuum) but larger than points, we have to be very careful about how we handle them, and we can create an even larger infinitude of sizes, including zero.