SQL Server sync databases between enterprise - web edition
What Neil has suggested is a viable option, but it is geared more towards Cloud environments and will be more complex than what you are trying to achieve.

OPTION 1 :

The simplest solution would be Transactional Replication (if you want near to real time data) or snapshot replication depending on your NEED.

You can use Replication from Enterprise Edison to Web edition. Important to note that web edition does not support PULL Subscription. It only supports PUSH Subscription. 

Depending on your business needs, you can schedule to sync every 1 hr or 1 day. 

Replication support matrix is here

OPTION 2

Use 3rd party applicaitons like Redgate schema and data compare for syncing data between 2 databases. It also has command line options, so you can write up your own custom scripts that will periodically sync data. You can get started here

SQL Server also has an inbuilt data sync functionality which is commandline called "TableDiff".

As you see, there are many options, which one will suffice your need depends on your Business requirements.