Minor reasons but a) it looks untidy (to me), and b) for example if I want to change:

    foo = {
        "bar": true,
        "baz": false
    }

to:

    foo.bar = true;
    foo.baz = false;

then I have extra quotes to delete. Those half seconds add up over a year!

I guess you could argue the opposite though, that this looks messy:

    let headers = {
        Expires: 0,
        'Content-Type': 'application/json'
    }

Which leads me to believe it's a matter of personal preference, and you should just pick one and stick to it :) And look, there's even an eslint rule for it: http://eslint.org/docs/rules/quote-props

Quoted keys allows more variety in the keys (e.g. "Content-Type") but is more annoying to use if all your JS code is written in camelCase (headers["Content-Type"] vs headers.contentType).