Why wall thickness matters more than infill
Where the strength of a printed part actually comes from.
Most of the strength in a printed part comes from its outer walls, the continuous printed skin wrapping the whole shape, rather than from the sparse lattice printed inside it, because a load applied to the part has to travel through whatever material forms a continuous path from one side to the other, and the walls are almost always that path.
What is really going on
A printed part's outer walls are laid down as continuous loops tracing the shape's boundary at each layer, while the interior is usually filled with a sparse repeating pattern, a lattice with far more air in it than plastic, whose job is mostly to support the walls above it while they print and to stop large flat top surfaces from sagging into open space. A force pressing on the part has to pass through solid material to get from one side to the other, and the walls, wrapping continuously around the whole shape, are almost always the shortest and strongest path available, whereas the interior lattice, mostly empty space with only occasional struts, offers little resistance unless the load happens to land directly on one of them. Doubling the amount of interior lattice adds weight and print time without adding much strength, because it was never doing most of the structural work, while doubling the thickness of the outer wall adds a genuinely stronger, continuous shell that the load actually has to travel through. A thin wall backed by a dense lattice can still crack under a load a slightly thicker wall backed by almost nothing would have survived easily, because the crack starts and spreads through the wall itself long before the load ever reaches far enough in to test the lattice behind it.
The egg comparison
An intact egg held in the palm and squeezed end to end along its length is remarkably hard to crush by hand, because the load travelling into the shell spreads around its continuous curved surface rather than concentrating anywhere, and a thin, unbroken shell turns out to resist a surprising amount of force this way. The same egg's shell, broken into flakes and packed loosely into a small bag, resists almost nothing, since the same quantity of material no longer forms one continuous path for a load to travel along, only a pile of separate fragments that slide and rearrange under the lightest pressure. A printed wall is the intact shell; a sparse interior lattice, however much plastic it contains, is closer to the bag of flakes. The eggshell test also shows why shape matters alongside thickness, since a shell squeezed end to end, where its curve spreads the load evenly, survives far more than the same shell tapped sharply at a single point, and a printed wall with a smooth, continuous curve resists a load more evenly for the same reason a flat panel of the same thickness would not.
The one number worth remembering
Adding a single extra pass of the nozzle to a wall, thickening it by not much more than the width of the nozzle itself, can add more real strength to a part than doubling the density of the interior lattice from a sparse fill to a much heavier one, because the wall is on the path the load actually travels and the lattice, however dense, still is not.
What follows from this
Because the walls do most of the structural work, a part that needs to survive real handling is better served by a small number of thicker, more numerous wall passes than by a high percentage of interior fill, and a part that keeps breaking despite a heavily filled interior is very often failing at a thin outer wall that the extra interior material was never able to help. Checking a broken part for where the crack actually started, almost always at the outer surface rather than somewhere buried in the lattice, is usually enough on its own to show which of the two was ever doing the real work.