Because of solar insolation, the system is not closed. In particular, we have a valve (CO2) controlling insolation and reflection. You would not argue that the effect of a Mylar sheet placed above a sunny swimming pool has to do with the mass of the Mylar.

Incidentally, it’s worth mentioning that, while I’m not an expert, I have several recent publications in hydrology, and I talk regularly with climate scientists and hydrologists about drought, including coauthors of the report I linked. The lines of argument you stated above are nonsense, I’m afraid. If you care about this subject, please do yourself the favor of reading some high-quality research summaries. It’s actually quite striking how much we do know about the Earth system.

Mylar is a non porous material. The actual greenhouse effect is caused by trapping warm air in as it is warmed from the water itself. The solar energy first enters the pool through the transparent material, warms the water, and then the warm water warms the air. The mylar traps the warm air from rising as it naturally would, where it would mix with colder air and cause another thermodynamic exchange.

CO2 does not act literally like a blanket over the earth, that's not how radiation works. If CO2 cannot retain the heat then it will be lost to space at night.

The closest thing to a true blanket effect would be clouds, although they have complex shapes and depending on where they are located in the atmosphere can have either a cooling or warming effect. They are made up of mostly liquid water and do vary according to solar activity through cosmic ray flux as shown in Svensmark's work. Link above.