We call them "weekly downloads" on detail pages, category browse pages, and search results. They're not really downloads; they're installations. What do we call 'em?

Sure, installs or installations - whichever fits on the buttons.

We discussed this on a thread back in January ("installs, downloads, and users") and the vibe seemed to be stick to what's easier to understand and what people are used to, e.g. downloads. Installations is ambiguous.