What Weighs More: 1 Kg of Iron or 1 Kg of Feathers?

Once, when I was still a child, my father asked me: "Which weighs more: 1 kilo of iron or 1 kilo of feathers?" I remember that sure of myself I answered him quickly: "Surely 1 kilo of iron weighs more, dad, because metal things, like the armor of medieval knights, are very heavy, while the feathers that decorate birds' wings are very light". I can't tell you how disappointed I was when I heard him say: "No my son, that's wrong: they weigh the same, because 1 kilo is always 1 kilo!" Maybe because of the evening trick questions from my dad, when I grew up I decided to become a physicist, and to my big surprise I discovered that I was right when I was a child. Indeed: On the Earth, even if only by a little, 1 kilo of iron weighs more than 1 kilo of feathers! Don't worry, the sawdust that I have in my head has not caught on fire! But I hope that I have made you curious and that now you will want to come hunting with me for this strange and heavy mistake.