I can't restore my database on SQL Server 2012. Exceeds size
Express Edition limits the size of the database to 10 GB.

The backup is small because it only contains pages that are used -- regardless of whether or not the backup is compressed -- but the original file sizes will be restored to the size they were when they were backed up. The file sizes are what count against the limit.

Assuming this is the problem, the only solutions are to shrink the files before taking the backup, or restore the backup on a different edition (probably Developer edition).