"This is an amazing service"
— Matthew Snider What They Say

Why do widgets at the bottom of Resurrect’s homepage not show in the order I expect?

Resurrect uses Masonry. Here is a description of how it works from the project’s website.

Masonry is a JavaScript grid layout library. It works by placing elements in optimal position based on available vertical space, sort of like a mason fitting stones in a wall. You’ve probably seen it in use all over the Internet.

With this knowledge, you can tweak the order in Appearance > Widgets > Homepage Bottom. Keep in mind that the size of the content in a widget can cause its order to change.