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