About the pressure, temperature, and weight of the atmosphere.

See this site:

http://www.newton.dep.anl.gov/askasci/wea00/wea00190.htm

I have an old airplane altimeter that I used to conduct the experiment that you described.
I placed it in the freezer first and then noted the pressure reading, then I placed in an oven that was first heated to 200 degrees.
The pressure difference between the cold and the hot areas was approximately one fifth of a foot in altitude.

The test is not very scientific because the moisture of the air in each location was not controlled and the reading was close to the resolution of the altimeter, but it does prove that the air becomes less dense and therefore exerts less pressure when it is heated in a open environment.