SQL Server 2008 R2 DB grows overnight and slow
I don't have answer but would like to clear few things that would help


  DB is 34GB, TL is 1.2 GB, 10% for both


There was surely something happened in database it cannot grow on its own. The first thing you should do is change autogrowth setting you have set autogrowth in percentage(10 %)  for both data and log files this IMO would have forced database to grow unnecessarily. You can refer to Autogrowth settings and how to configure it and configure optimum value for this preferably in MB.


  It's typical to see it run at around the 6-8 GB range but all of sudden its taking up to 24 GB of the 32 GB the server has. Again unexplained. 


What is current max server memory setting and please dont change it to lower value it will cause issues for you. Its normal for SQL server to utilize all memory if allowed to use via max server memory setting.