There are many potential causes of your problem, but I doubt that it is because your inbox is too large...unless you have exceeded the amount of space that AOL alots you. You can check this by checking your email account status online.
Before we go the restore route, let’s double check your settings in Mac Mail. Check the link below for what the settings should be:
If that does not help, then let’s try the restore option:
I currently do not have my Mac with me, but I believe Time Machine is fairly intuitive to use. Please check the following overview to see if it is enough information to get you started. I would suggest restoring your whole system to the date you are confident is prior to the problem: