SQL Server Express Instance Memory vs Memory Limit
Community wiki answer:

The 1GB limit is only for the buffer pool, SQL Server uses other memory pools as well so it is possible to see memory usage over 1GB. 

Quoting from Memory configuration and sizing considerations in SQL Server 2012 and later versions


  Starting with SQL Server 2012, these memory limits are enforced only for the database cache (buffer pool). The rest of the caches in the SQL Server memory manager can use much more memory than is specified by these edition limits. For example, a SQL Server 2012 Express edition can use only a maximum size of 1.4 GB for its database cache. Other caches (such as the procedure cache, the metadata cache, and so on) can consume memory up to the size specified by the "max server memory" configuration.


For SQL Server 2016 SP1 onward, Express can also use an additional 352MB for columnstore segments per instance and another 352MB for in-memory OLTP (Hekaton) objects per database.

The maximum buffer pool size was also changed in the documentation from 1GB to 1410MB for SQL Server 2016, though this probably applies from SQL Server 2012 (where the big memory management changes were made).

Only the buffer pool, columnstore cache, and in-memory OLTP cache sizes are restricted by quota. Other cache stores and memory consumers in Express Edition can push overall memory usage up to the configured limit in the max server memory configuration setting.

See Also:


Why does SQL Server 2012 Express use 9.5GB of RAM on my server?
Does SQL Server 2008R2 Express actually enforce the memory and CPU limit?