Suppose we put a very obese man inside a large air tight room with a treadmill and he runs on the treadmill for 24 hours and at the end of the day he sees his weight has come down (mostly water weight, but also includes some fat), would the weight of the entire sealed room be decreased?
No. Providing the room is airtight, the weight of the room will stay exactly the same else the conservation of mass law will be violated ( but it would be more complicated if the room is not airtight ) .
As the man looses mass because of water loss and fat loss, the water will turn into water vapour in the air ( which will, incidentally, increase the air pressure providing the room is airtight ) and the carbon in the fat will replace some of the oxygen in the air in the form of CO2 which is heavier than oxygen and will make the air become more dense.
So the overall effect is that some of the mass from the man will be transferred to the air in the room thus, providing the room is airtight, the mass of the whole room including the air inside will stay the same and therefore its weight will stay the same.