Image loses quality when set as a background

I’m trying to set a image as a background in a way that it fits different resolution browsers. So it needs to be big to start with.
I uploaded an image, but it looked blurry – and I had photoshoped it and used smart sharpen, so I knew that wasn’t the problem. I figured maybe it’s because it was too heavy, since it was png, so I saved it as jpg. No improvement there.
I thought WP might be compressing it, or something, but I decided to take a look at the uploaded image, and it actually looks perfectly fine, even in png. You can see it here: https://castlebrasil.com/site/wp-content/themes/nutty2/img/header.png
But still, on the site, it looks quite bad: https://castlebrasil.com/site
I use a secondary background on pages/single posts. It has the same width, but no the same height. But it looks perfectly fine: https://castlebrasil.com/site/a-serie/spoilers/ (original: https://castlebrasil.com/site/wp-content/themes/nutty2/img/header-fixo.png)

What’s the matter?
Is there anything I can do to make the background keep the original quality/resolution?