Actually... all air has weight. That it doesn't weigh much does not mean it is weightless 
Different air has different weight. An interesting thing about our body: we breath oxygen (and other gasses) in... and breath CO2 (and those other gasses) out. I do not know how much weight was supposedly lost by the bodies when they died... but I think that losing the weight of the contained air is accumulative with whatever else is responsible for the loss in weight. Supposedly not much weight was lost in the study... and air does not weigh much. So it could easily be partly (or fully?) responsible for the weight lost.
A vacuum would have nothing within it... so there would be no weight.
Different air has different weight. An interesting thing about our body: we breath oxygen (and other gasses) in... and breath CO2 (and those other gasses) out. I do not know how much weight was supposedly lost by the bodies when they died... but I think that losing the weight of the contained air is accumulative with whatever else is responsible for the loss in weight. Supposedly not much weight was lost in the study... and air does not weigh much. So it could easily be partly (or fully?) responsible for the weight lost. A vacuum would have nothing within it... so there would be no weight.
Please give me a home where cloud buffalo roam
Where the dear and the strangers can play
Where sometimes is heard a discouraging word
But the skies are not stormy all day
