This makes an html list and puts it into a div (or some element you aren't showing here) with id of weather... So take this out:
html = '<h1 class="icon-'+weather.code+'"></h1>';
html += '<h2 class="weather-temp">'+weather.temp+'°</h2>';
html += '<ul><li>'+weather.city+', '+weather.region+'</li>';
html += '<li class="currently">'+weather.currently+'</li></ul>';
//html += '<li>'+weather.tempAlt+'°C</li></ul>';
TO:
$("#display-location").html(weather.city+', '+weather.region);
$("#current-weather-column").html(weather.currently);
And so on
Basically you create an html div (or other element), give it an ID, then reference that ID using the above format ($"#ID") To then populate it's internals, you use .html(text_and_html_you_want_in_the_element)