Fluids exert hydrostatic pressure because their molecules hit each other or the immersed body, but why is that at a greater depth pressure is higher when molecules are the same ?

Assume density of fluid is uniform throughout the liquid.
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Your statement: 

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> Assume density of fluid is same throughout.
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conflicts with your actual question 

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> But why is that at a greater depth pressure is higher when molecules are the same?
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If we imposed the very strict and non-physical constraint that the density of the fluid was uniform and isotropic, then we would have not variance in pressure what so ever - but as I have said this is non-physical. 

What happens in reality is as follows... Each molecule in a given fluid has a mass. Gravity acts on this mass (lets assume vertically, and a column of perfectly stacked molecules) to produce a weight for each molecule. If we take the limiting case where all molecules are stationary then it should be easy to convince yourself that at some depth within the fluid a given molecule has a force acting upon it purely from gravity $Mg$ [$M$ is the molecules mass] plus the weight of all those molecules above it $\Sigma\_{i}m\_{i}g$ [where $m\_{i}$ is the mass of the ith molecule], but also a reaction force provided by the contact with the molecule directly below it $R$, where 

$$R = Mg + \Sigma\_{i}m\_{i}g,$$ 

for some arbitrary stationary molecule. From this it should be clear that the absolute force acting on this molecule (in the vertical direction, for our ideal column) increases with the depth of the molecule. This is essentially what causes pressure in a fluid, in increases the fluid density with depth. 

*Note. Of course the above is very much simplified as there will be much more going on at the molecular level, but this example should provide you with a basic Newtonian view with which to build from.*

I hope this helps.
In short: because the weight does it so.

Imagine a situation where several people are walking on each other in a small room: those that are at the top don't feel any discomfort whereas those at the bottom are crunched by the weight of the one above them. It's quite the same for the molecules.