Ozone is above, nitrogen is below
The entirety of the Earth's atmosphere can be divided into two regions: the homosphere and the heterosphere. The former extends from the earth's surface up to about $\pu{100km}$.  Within this region, turbulence and mixing, even within the relatively calm, persistent temperature inversion known as the stratosphere, prevents any segregation of gases based on molecular/atomic weight.  With the exception of water vapor, the composition of the major constituent gases only varies by a few hundred ppm from any given region of the homosphere to another.  

The heterosphere extends from about $\pu{100km}$ above the earth's surface upward until merging with the interplanetary medium at around $\pu{100,000km}$. Within this region, the mean free path of any gas is great enough that gravitational forces have a chance to segregate the different species based on their mass, rather than by bulk processes like turbulence.  

The Encyclopaedia Britannica describes the heterosphere this way:  


  In the heterosphere, the concentrations of the heavier constituents,
  such as nitrogen or oxygen, decrease more rapidly with increasing
  altitude than do the concentrations of lighter gases, such as hydrogen
  or helium; and eventually the atmosphere is dominated by the lighter
  gases. Under mean daytime conditions, helium and its ion become
  dominant around $\pu{1,000 km}$ ($\pu{620 miles}$) and hydrogen and protons above
  $\pu{2,500 km}$ ($\pu{1,555 miles}$).


At sufficient altitude, $\ce{H+}$ becomes the dominant species and hydrogen is the only element of significance that escapes the atmosphere based on its low mass.  

So, to reiterate the answer to the question; the troposphere and stratosphere both lie well within the homosphere, and thus segregation based on mass plays no roll in their distribution throughout this region of the atmosphere.