Fatman, the plutonium implosion bomb that was detonated over Nagasaki, used only 6.2kg of Pu. Also, the Pu-239 used in weapons doesn't require a lot of shielding. There are plenty accounts of people handling nuclear weapon cores that have had only a light plating of other metals or with only thick gloves.

What probably is quite heavy is all of the associated components that you need to make a bomb - the chemical explosives, tamper etc.

The W54, one smallest nuclear warhead anyone is admitting to making, was about 23kg - although this did have a very small yield.