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Think of the genes as like the blueprints to a house. Blueprints are just made of paper and fairly light, but have the information. Now consider the house, which is like the protein. The protein is the thing that gets stuff done inside the cell, like digest things and support the cell. Similarly, your proteins are much heavier than your genes.
I disagree with Kainui: the DNA itself is made up of nucleotides and the average molecular weight per base pair is 660 Daltons. Each amino acid is coded by three nucleotides, so that's about 2000 daltons per amino acid coded. The amino acid itself is probably less than 200 Daltons on average so the protein is bound to be lighter. If you consider an eukaryotic gene then there will be long stretches of non-coding sequence (introns) between the protein - coding exons so eukaryotic genes are much heavier.