Any ideas as to how much it costs to host?

No clue. But given that it’s a domain for a major piece of open-source software with millions of users, my guess is it’s a pretty large bandwidth site, so probably has a pricetag beyond “ye olde cheape hostinge companie” that hobbiests can afford. (It doesn’t seem the sort of thing that would normally be made public.)

If you’re wanting to get in touch with the developer, to ask about what it would take to get rid of the advertising, Don makes his email contact info easily findable on the main Notepad++ website

Because the developer lives in a capitalist society, where luxuries like web hosting with huge bandwidth usage costs money.

update: Snark aside, it really is because of the cost of hosting. And if you don’t want to see those ads, you could always just use https://github.com/notepad-plus-plus/notepad-plus-plus/releases/latest to find the downloads for the latest release on the ad-free GitHub interface, and https://github.com/notepad-plus-plus/notepad-plus-plus/releases to find any of the older releases back to 6.7.9, or https://github.com/notepad-plus-plus/old-releases/releases/ for releases older than that, back to 1.0.

A while back, he tried to make it better, by adding some CSS/etc, to make it more obvious that the ads were ads, not actual download links… but he is limited in what his host allows him to do.