Yeah this is my understanding, when you run a marathon - because your muscles require energy, your cells burn more ATP (energy)- which makes the TCA cycle go faster (the mitochondria in your cells physically burn ATP at a faster rate) which generates more CO2 (one of the bi-products) so you breathe faster, hence exhaling more CO2. If you simply sit down and breath fast - nothing other than dizziness will occur, as your muscles don't need oxygen and your cells aren't producing much CO2 to exhale.
As to the original question - if you eat 1Kg of food, yes you'll temporarily gain 1Kg of weight, but it depends on where the calories that make up that food come from, if you ate 1Kg of sugar - because of the effects on your blood glucose level, it's going to drive an enormous amount of insulin release - which ultimatley is going to end up with your liver converting a big chunk of it into fat (because that's all it can do when faced with an onslaught of 500g of fructose, remember sugar is 50% glucose, 50% fructose) and so out of that 1Kg, a good proportion of it will go into fat.. If you ate 1Kg of nuts, you'd weigh 1Kg more right away - but a far lesser amount would end up as fat, as it's metabolised in a far less-aggressive way - so whilst both foods weigh the same, even if both foods had the same calorie count, with the sugar you'd pile on the weight, not so much with the nuts.
