There are two ways to access folders - "as needed" which you're doing and by setting particular folders to sync "all the time" (like Inbox etc).
"As needed" folders are shown below the "set to sync" folders, to separate the two.
"Set to sync" folders are sorted by type and then by name.
I see. Out of curiosity, how can I change a sync "as needed" folder to sync "all the time"? Based on your description, I thought that checking "Use IMAP Push" would do it, but it doesn't seem to.
"As needed" folders are sorted by last access time: most recently accessed closer to the top.
Okay, that might help me work around the problem. If I can I configure certain folders to sync "as needed", the most recently used ones ought to appear at the top of the list. That's not quite as good as having the most often used ones first, but it's better than what is happening right now. Is there some way to do this? The only sync-related options I see for these folders seem to be for treating them as incoming, spam, deleted, drafts, or sent, which they are not.
You can change how long a particular folder stays on this "recent list" and how many entries are allowed -- app settings under account list (but it affects the "recent folders" list everywhere else, such as in the dialog you have on your screenshot).
That might also help a bit, if I could set this list to be 0 entries, but the app doesn't let me set a recent folder count value below 3. Drat.
Aha! I just found a thread from two years ago with other users having the same problem. (It looks like one of AquaMail's earliest feature requests, actually.) I look forward to seeing the manual sort feature mentioned here:
http://www.aqua-mail.com/forum/index.php?topic=26.0