University Physics with Modern Physics (14th Edition)

For an interference maximum, $2d sin \theta=m \lambda/n$, so $sin \theta$ is proportional to $\frac{1}{d}$. If d is smaller, the sine, and thus the angle, are both bigger. The microspheres are more tightly packed at the bottom (smaller d) than at the top, so the interference maximum occurs at a larger angle.