It does become heavier but negligible.
a) Millions of tons are emitted but millions are also recycled or removed. Plants and planktons use CO2 and convert to oxygen. Millions of tons more are converted or captured by the ocean.
b) CO2 concentration is about 0.04% (420 PPM) of the atmosphere. Pre-industrial age that was about 0.03% (280 PPM). This shows how delicately balanced this cycle is. Even a small shift might result in large climate impact.
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