Since you mentioned image copies, I assume you are running DB2 for z/OS.
If you were to do weekly reorgs, and then runstats right after, then the runstats would not reflect the "average" state of the database during the week, so I might run reorgs on the weekend, and run runstats Tuesday night, to get the average state of the data during the week. Runstats (unlike reorg) can be done with little or no interference to applications.
And if your tables are not rapidly growing or shrinking, you could probably get away with doing the Tuesday (mid-week) runstats once a month, or even less often for tables that don't change much. For programs that use static SQL (most COBOL, PLI, Stored Procedures, etc), then the access plan would not change anyway unless there was an explicit rebind of the plan or package involved.
Many people who do not work in the mainframe world fail to understand that in most companies the z/OS jobs are charged back to an account, and that such jobs are not ""free", and in fact can be quite expensive.