Here's a slightly more compact solution to the problem:
const typeSizes = {
"undefined": () => 0,
"boolean": () => 4,
"number": () => 8,
"string": item => 2 * item.length,
"object": item => !item ? 0 : Object
.keys(item)
.reduce((total, key) => sizeOf(key) + sizeOf(item[key]) + total, 0)
};
const sizeOf = value => typeSizes[typeof value](value);