The ranking only effects the map markers and results…not the search box category selector, I misunderstood what you were asking about.
After looking at your link. You are asking to rearrange the “Search by category selector ” is that correct? you currently have the checkbox vertical selected.
By default that is going to be shown alphabetical.
If your developer is skilled using CSS,jquery, and the theme you are using allows for it, they might be able to write some rules to change the layout of how the selector orders them.