Solution

As a matter of fact wood is "heavier" in a vacuum. But why is it so?

Since the wooden chunk has got a greater volume than the chunk of iron,
according to the Archimedean Principole, the two bodies are both affected by buoyancy of different degree in the air, which counteracts their weight force:

Due to the fact that the wooden chunk is affected by greater buoyancy because of its greater volume, it has to be slightly heavier to compensate the difference. Otherwise the beam balance would not be in equilibrium.