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It's Sulphur.

The weight of sulphur decreases when it turns wet because suphur is a hydrphobic substance. The apparent weight of hydrophobic substances under water seems to be much less than the real weight. (considering the apparent weight here to say it's lighter and not the real weight - just to satisfy the terms of the riddle)

On burning, sulphur turns into it's oxide form.
Due to the presence of oxygen, the compound weighs more than just sulphur.
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It's sulphur. When it get's wet, it gain's the double of it's weight, and when it is burnt, it gain's twice it's weight,