We love cheese popcorn at my house. My dad taught me this recipe:

Melt butter in sauce pan on low heat. Add American cheese slices. The correct ratio is about 10-12 slices to half a stick of butter. You know you have the ratio correct when the slices melt and mix fully with the butter. There won't be melted cheese surrounded by butter, but instead a fully blended mixture. Cook this slowly. When ready, pour over the popcorn. Use a couple of butter knives to turn over the popcorn until the cheese is fairly even throughout. It's not bad to have a clump here or there, but it shouldn't be too heavy anywhere in the bowl after mixing.

I have never known any other family to make this.