In general, if the "messages to sync" setting is high, the app has to do more work (still 6 GB in a few days for an AOL account is just way our of this world). The default for IMAP accounts is "50", please long press on the account -> options and folders -> check "messages to sync".
Yes something could be wrong in the app, but I've also seen users set "messages to sync" to "thousands" and mail check schedule to "every 5 minutes", and well...
For Exchange:
Please check the above setting too. For Exchange specifically, a "messages to sync" set to date based value (e.g. "14 days" or "21 days", not "25 messages" or "50 messages") is more efficient in the long run, but requires more work up front on the first mail check, esp. if the mailbox has a lot of (say tens of thousands) of messages.