My .EDB file grows when I search.
When doing a WebDAV or any other search, you will likely see the .EDB file expands.
When performing a search against a mailbox using WebDAV or any other API, you may see the .EDB file grow in size. Don't panic, this is normal. When a search is performed, Exchange will put the results into a search folder. When the same query is re-issued, the results can be reused. Also, some properties may get promoted from the .stm to the .edb when requested in a search.
Exchange Storage Architecture
https://technet.microsoft.com/en-us/library/bb124808.aspx
Private Information Store log files grow when a user performs a search in OWA
https://support.microsoft.com/kb/811650/en-us