add_theme_support call for the custom header support. Even if you change the size there (in a child theme), you would need to adjust the CSS so that a bigger image works with the rest of the layout.your website container 1280px but navigation menus is very big.
I think it is important to increase header navigation in your website and header image size is good.
Navigation Menu CSS
.menu-blog-container ul#nav li > a {
padding: 7px 20px;
margin: 0;
position: relative;
}
.menu-blog-container ul#nav li > a::before {
margin: 0px;
left: -3px;
position: absolute;
}
.menu-blog-container ul#nav li > a::after {
right: 5px;
}
nav.menu-primary > .container > .menu {
text-align: center;
float: none;
font-size: 0.7em;
}
nav.menu-primary > .container {
max-width: 100%;
}