If the nitrogen and oxygen in our atmosphere were doubled would the pressure double?
The surface pressure is just the weight of the atmosphere per unit area, so yes.

The density decreases with altitude so there is no well defined "top" to it. Assuming constant temperature (Isothermal-barotropic approximation) the density decreases exponentially with altitude.



If it were doubled there would the same portion of mass above any given altitude (but more mass above any given altitude).