It looks like you want to maintain the state of your toggled class between sessions which could be done with Cookies but would perhaps be better suited for localStorage.
For the sake of completeness I'll demonstrate both approaches
With Cookies
To better understand the distinction between Cookies and Local Storage see this question, but I honestly think you could go with either approach. One advantage Local Storage has over cookies in this case is that you wouldn't need an additional library.
let state = Cookies.get('toggle');
$(body).toggleClass('.blackout', state)
With Local Storage
let state = localStorage.getItem('toggle');
$(body).toggleClass('.blackout', state)
With your updated snippet
var toggleLocalStorage = localStorage.getItem('toggle');
var toggleStatus = toggleLocalStorage ? toggleLocalStorage : false;
$('#boToggle').on('click', function(e) {
$('body').toggleClass('blackout', toggleStatus);
localStorage.setItem('toggle' toggleStatus);
});