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.
First, think of this in terms of psi:

This is a bit simplified, but: When you are standing at sea level, under S.T.P (Standard Temperature and Pressure), you have a column of air some 120,000 feet high pushing on you. That weighs 14.7 pounds. (for a column that has a cross-section of one square inch.)

That is the pressure we feel, every day. It is what our bodies are accustomed to. 

Now, think in the same terms, when you are under the water. In addition to that column of air, you also have a column of water--however deep you are-pushing down on you. If you are 33 feet deep, a square-inch cross-section of water will weigh as much as the column of air above it... Which is why at 33 feet, you are now experiencing 2 Atmospheres of pressure. (Atmosphere being the equivalent of what you feel at sea level at STP)