Please do some numbers on this.
The pressure at the center of the Earth is immense--somewhere between 3 and 4 million times the pressure of the atmosphere at the Earth's surface. To assume that a small loss in atmospheric pressure, measure in a few pounds per cubic inch, would cause any measurable decrease in the gravitational load that creates this core pressure is ludicrous. The idea that macroscopic gas bubbles could exist at this pressure, at almost ANY temperature, is ludicrous.
This is like saying a mountain climber stepping on the top of Mount Everest is going to suddenly shorten the mountain by a thousand feet.
This stuff doesn't stand up under even the most rudimentary examination.