The force that causes fluid pressure to vary with depth is the weight of the fluid. As the fluid is a form of matter, it has weight and it exerts a force due to its weight. This force is known as hydrostatic force or pressure.
When the fluid is at rest, the weight of the fluid acts vertically downwards and it exerts pressure on the bottom of the container or on any object submerged in it. The deeper the object is, the more fluid is above it, and the greater the weight of the fluid is, so the greater the pressure is.
This happens because of the concept of Archimedes' principle which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid that the object displaces. So the deeper an object is submerged in a fluid, the more fluid it displaces, and the greater the buoyant force is. This buoyant force also known as the upthrust is what opposes the weight of the fluid and causes the pressure to vary with depth.