The bak files are created when eM Client does a database repair after an incorrect shutdown or some other database error. These files are not needed for normal use.
What you can do is close eM Client and run C:\Program Files (x86)\eM Client\DbRepair.exe to check that everything is fixed, then open eM Client and make a backup, just in case. The backup can be done in Menu > File > Backup. Then after closing eM Client again, delete the bak files. Actually, restoring the backup will remove the bak files also and clean up the database, so that might be an easier and quicker option. That will reduce the database size to almost half.
Using IMAP with downloading messages for offline use not selected, will result in a fairly small database. That is because the message bodies will stored on the server rather than on your computer. There are some disadvantages to that as when there is no Internet connection you will not be able to view the message body, and it may take a second or two to open large messages when you click on them. The setting can be changed in Menu > Tools > Accounts, then in the Synchronization section of the IMAP tab. I am not sure if this will reduce the database size if the offline data has already been downloaded, but it will not grow much afterwards…