Why should the surface deform?

1. Because a heavier fluid is on top of a lighter fluid,
2. Because of spreading of a fluid on a non-wettable surface.

A point to be noted is that these are not equilibrium situations.

Figure 3.5. Thin film being coated on a surface

Weak flow in the bounding fluid means that pressure distribution is hydrostatic.
Also note that the mean film thickness is constant because of conservation of volume.

is a constant and