Is the iron loss of an iron core transformer twice the mass of the iron core?
How is kg converted into watts?

By making some assumptions. Presumably the author had some operating field in mind (loss increases with the maximum field applied), an operating frequency (loss increases with the frequency), and a particular grade of core material (as you spend more money on thinner laminations, exotic alloys, and careful heat treatment you can reduce the losses somewhat below those of a cheaper core). 

Once you find out what these assumptions are, you can make sense of his watts per kg multiplier.