You're misunderstanding what 4% in system settings -> battery means.
It means that Aqua was responsible for 4% of battery charge used over the reported period -- *not* that AquaMail used 4% of total battery capacity.
On all my devices, the unquestioned leader is the screen.
If a phone has been just laying around, not used, then it's WiFi, "Phone idle" and "Cell standby". Oh, and "Android OS"
I also see from your screenshot that you've got at least 4 folders in push mode. This is quite a lot, I usually recommend push only for the INBOX folder and maybe 1-2 others.
IMAP IDLE (push mail) can be expensive, but don't take my word for it:
http://www.emailsfromstevejobs.com/2010/06/06/imap-idle-support-its-a-power-hog/Given the circumstances, you're getting really low battery use by Aqua.
I'm also not sure that the "309" number, reported by your third party app, is correct.
BTW - why does Google Play Services -- keeping the CPU awake about 3X more and having 4X the number of wake locks -- not bother anyone?