Transactional Replication guidance
There are many ways  by which you can transfer data and all depends on this part of question..


  copy them regularly to a SQL Azure database


1.If you want once a day,you can write ssis package and do the logic of checking/merging data in that

2.You also can write C# program which does this for two tables and run this through SQLServer agent..

3.if you are looking for near realtime data transfer,i would go with Transactional replication.This is supported now..

Setting up is very easy task and same as Onpremises ,but with one exception of no pull subsribers .

This article from Joe Sack will help you on how to set up..

There are also some limitations which you need to account for..

The publisher and distributor must be at least at one of the following versions:

SQL Server 2016

SQL Server 2014 SP1 CU3

SQL Server 2014 RTM CU10

SQL Server 2012 SP2 CU8


You can read this link for more details..