Why does my transaction log use so much space?
Transaction logs are, as far as I'm aware, not stored in what we would consider a very disk space friendly manner.  This is because the logs have to be able to do several things.  Almost all the neat tricks of ACID compliance are not because the database data files exist, it's because the transaction log files exist.

Think about some of the things the logs have to do:


Allow a transaction to be rolled back to the state the database was in prior to the query running.  This means the database has to know not just what was in place, but how to get back there.
Keep the rest of the queries and transactions running from interfering with or being interfered by the query you're trying to run.  Even if you're not doing these kinds of things, the database will do them unless you specifically tell it not to.  The database engine needs to be able to seamlessly treat data not yet written to the database as though it were and as though it weren't.  Potentially at the exact same time.  
The database employs write-ahead-logging, meaning it will write everything to the log before the transaction is considered complete.  Note that committing a transaction doesn't write the data to the database.  It means it's finished write-ahead-logging!  This means the data is first written to the log, and then later is copied to the actual database.  Writing data to logs is necessarily faster at the cost of not being space-efficient.
Assuming you're using the full recovery model, the database logs must support point-in-time recovery.  This means the system has to be able to recover the database to a specific point in time at all times regardless of what the database has undergone.  So the transaction logs would have to show how to recover the database to how it was before your massive query as well as after it.  This is different than the need to be able to rollback the transaction.  This is about recovery hours or days after the data has been committed.
Save to disk all of the above as fast as possible because performance is really important, too.


You may find it useful to read about the transaction log architecture.  It's really, really not surprising that transaction logs eat up so much disk space.  

A database I work on is about 5 GB in size.  We restored the DB to a testing area so I could test log growing.  This was on a DB using Simple recovery.  One table in this database is about 2.5 million rows and is about 5% of the database.  It has a clustered index for the primary key, but no other indexes, foreign keys, triggers, or check constraints.  I ran two statements, essentially update bigtable set int_field = int_field + 1 followed by update bigtable set int_field = int_field - 1.  This does nothing at all but creates an awful lot of work for the database, especially because int_field is part of the clustered index.  Each execution caused the transaction logs to grow about 1 GB.

I'm assuming you ran (essentially):

insert into production.table (id, field, ...)
select id, field, ...
from staging.table


That will work, but it means the database has to keep track of an awful lot by default.  However, you can use it in a minimally logged manner that will help a lot.  If you really have to do this kind of thing, here's what I would do:


Do a full backup of the DB and logs.
Set the database to single-user mode.
Disable any nonclustered indexes on the target table.
Set the recovery mode to bulk logged.


From here, I'd follow MS's best practices for using INSERT INTO ... SELECT for large operations with minimal logging:


  Using INSERT INTO…SELECT to Bulk Import Data with Minimal Logging
  
  You can use INSERT INTO  SELECT  FROM
   to efficiently transfer a large number of rows from one
  table, such as a staging table, to another table with minimal logging.
  Minimal logging can improve the performance of the statement and
  reduce the possibility of the operation filling the available
  transaction log space during the transaction.
  
  Minimal logging for this statement has the following requirements:
  
  
  The recovery model of the database is set to simple or bulk-logged.
  The target table is an empty or nonempty heap.
  The target table is not used in replication.
  The TABLOCK hint is specified for the target table.
  
  
  Rows that are inserted into a heap as the result of an insert action
  in a MERGE statement may also be minimally logged.
  
  Unlike the BULK INSERT statement, which holds a less restrictive Bulk
  Update lock, INSERT INTO…SELECT with the TABLOCK hint holds an
  exclusive (X) lock on the table. This means that you cannot insert
  rows using parallel insert operations.


Once I was done, I'd undo the three steps I'd done above.  I'd revert the recovery model, index and single-user mode change, and do another backup.  You'll then probably want to rebuild your indexes.

I'm not sure if you actually need to change the recovery mode to bulk logged to get some advantage from the minimal logging.  I've never had to do exactly what you describe, so I can't be sure.