Why does my SQL Server database triple in size after deleting millions of records?
You are doing two giant deletes, each one occurring inside an implied transaction.  Each record being deleted is first written to the transaction log. 

Because you have changed the database to be in simple mode, the transaction log will be truncated on checkpoint, but you are still causing it to grow during each delete statement.

I suggest you break up the deletes into chunks.  Inside a loop, you can delete one day at a time, starting with the oldest data, stopping at the 6 month mark.  (make sure you have indexes that support your delete criteria, create them if you have to, drop them afterwards).

This way, the checkpoints will occurr more frequently, thus keeping the size of the transaction log down to a minimum.

Truncating a table will NOT grow the database.

Also, before you issue the delete statements, make sure you find out if any triggers exist on that table.