I see your logic, and at first glance I was about to defend your statement, however it's not correct because:

1. If you burn pure carbon, you get O2 + C = CO2. That's the same number of gas molecules after burning. 1 gas molecule in the input, 1 gas molecule on the output. A gas's volume is determined by temperature and number of molecules, not the number of atoms(technically an approximation, but a very good one). Yes there are more atoms making up the gas, but once the combustion gas has cooled to ambient, the volume of CO2 is basically the same as the volume of O2 you started with. While the CO2 is heavier, this doesn't equate to more gas, it's just heavier gas. (If I give you a litre of petrol and a litre of water, you've got the same amount, although the water weighs more.)

However this is kind of moot because:

2. All this combustion can actually make he atmosphere weigh less and have a lower volume! Most of the stuff we burn is a hydrocarbon. Hydrocarbons burn to produce CO2 and H2O. The H2O precipitates out of the atmosphere, so there's actually fewer gas molecules in the air because we've removed oxygen and turned it in to water. In addition, the mass of the oxygen precipitated, is greater than the mass of carbon added, so the air is lighter too. Now it really depends what hydrocarbons we've burned. Natural gas (methane) produces twice as many water molecules as CO2 so would have the strongest depleting effect. Liquid fuels like petrol, diesel and oil produce about equal numbers of CO2 and water molecules so more slightly deplete the atmosphere. Coal produces fewer water molecules than CO2 I haven't done the math on whether this is a net mass increase or decrease (I expect it's pretty mass neutral) but it definitely still decreases the air's volume.