Check out line 2208 in your css and you’ll see how they setup the header width –
.site-header {
margin: 0 auto;
max-width: 1140px;
}
You can change or adjust there.
The header widget area can be found on line 2285 and looks like this –
/* Widget Area
--------------------------------------------- */
/* for main nav- widget area */
.site-header .widget-area {
color: #ddd;
float: right;
text-align: right;
width: auto;
margin-top: 12px;
}