That's a pre-Overground relic: Forest Hill and Sydenham were added to what used to be "fast" trains (the "Tats and Cats" I think*) many years ago, and then Brockley and Honor Oak Park to give them a 15 minute service.
There was indeed a period when Penge W and Anerley were closed on Sundays as an economy measure, so the differential pattern made some sense.
(*Sorry, Tattenham Corner and Caterham services, which used to split at Purley)
I remember the semi-fasts on the Sydenham slow which I think started to call at Brockley and HOP in the mid 90s? (They were I think the off-peak Charing Cross services until the timetable revision)
More recently, up until May 2010 the Caterham's did the fast between Sydenham and Norwood Junction.
Hard to believe that as short as 4 or 5 years ago, there were fast peaks between London Bridge and Forest Hill.