Physical meaning of variation of force of pressure with altitude in fluid We usually prove that pressure is a function altitute Z. Imagine a cube in a fluid, then the force of pressure on the bottom surface is higher than the force of pressure on the top surface. But we don't say how to explain this on a molecular level, does molecules of fluid move more on the bottom and hit more the bottom surface?
 A: 
does molecules of fluid move more on the bottom and hit more the
  bottom surface?

Given the same temperature at the top and at the bottom, the molecules don't move more, so there must be another mechanism in action.
In general the fluid at the bottom is compressed under the weight of the fluid above it. 
For gases, the compression is significant and, as a result, their concentration or density at the bottom increases. So, even though molecules may move at the same average speed, they are going to collide with each other or with a pressure sensor more frequently, leading to a higher pressure.
For liquids, which don't compress much, the density practically does not change with depth, but even insignificant reduction of the distance between molecules leads to a significant increase in the repulsion forces and, therefore, pressure. This type of reaction is even more convincing in solids: if we put a book on a table, we don't observe any deformation of the table surface, but, since the book does not fall through, we have to conclude that the surface of the table has deformed or compressed just enough to produce a sufficient reaction force or pressure to balance the weight of the book.     
A: We do. The most basic explanation is that the lower ones must hold the weight of the ones above them. The more deep, the more weight above them.
Edit: think about a tower. The upper bricks must only deal with their own weight. The lower ones must deal with theirs, and also the ones from upside. Have you ever jumped onto a friend's back? It's the same. The one above only holds its own weight, but the lower one must hold the total weight.
The lowest part is supporting more weight, weight is a force. Dividing it by the area, you've got a "gravitational pressure", which adds to the pressure there might already be there.
