Yes, but the weight of the oxygen is in the atmosphere already. And for a bonus, all the hydrogen you burn removes O2 from the atmosphere in the form of water,

Yes, but the weight of the oxygen is in the atmosphere already. And for a bonus, all the hydrogen you burn removes O2 from the atmosphere in the form of water, reducing the weight of the atmosphere (and therefor the greenhouse effect of the atmosphere). How much the reduction of O2 from H burning offsets the transformation of O2 to CO2 is left as a problem for the reader. If anyone knows of a paper that discusses this effect, I'd love to read it.