Going back a little further, the 1991 timetable shows an actual London Waterloo to London Waterloo via Addlestone service.
It ran at 0635 from London Waterloo, all stops via Hounslow, had a three minute dwell at Virginia Water leaving at 0733, and ran into Waterloo via Weybridge.
The effect of the service in this path appears to have been to allow a train to run non-stop from Walton-on-Thames to Waterloo directly in front, with the Virginia Water starter picking up the stations between Walton-on-Thames and Surbiton.
Notable is that today, the service from Weybridge to Waterloo via Surbiton is somewhat more sparse than it was in 1991.
1991 departures between 0700 and 0805 were
0714 53 0642 Farnham to Waterloo 0748 (all stations to Surbiton, Clapham Junction)
0730 75 0710 Guildford to Waterloo 0803 (all stations to Surbiton)
0742 63 0655 Basingstoke to Waterloo 0809 (fast from Walton-on-Thames)
0746 13 0733 Virginia Water to Waterloo 0818 (all stations to Surbiton)
0755 53 0722 Farnham to Waterloo 0830 (all stations to Surbiton)
0805 10 0755 Woking to Waterloo 0838 (all stations to Surbiton)
2023 departures between 0700 and 0805 are
0711 10 0702 Woking to Waterloo 0745 (all stations to Surbiton)
0737 10 0725 Woking to Waterloo 0815 (all stations to Surbiton)
0743 64 0706 Basingtoke to Waterloo 0807 (fast from Weybridge, previous stop Farnborough)
0800 10 0746 Woking to Waterloo 0836 (all stations to Surbiton)
Just dug out my reprint of last Southern Railway timetable (October 6th, 1947 until further notice)
Trains from Weybridge (weekdays)
03:11 Walton, Esher, Waterloo only
05:46 ex Guildford 05:22, all stn Surb, then Wim, ClapJ, Wat 06:20
06:16 ex Guildford 05:52 all to Surbiton then Waterloo 06:46
06:46 ex Guildford 06:22 all to Surbiton then Waterloo 07:16
07:16 ex Haslemere 06:29 all to Surbiton then Waterloo 07:46
07:25 ex Woking 07:16 all stn to Surbiton then Waterloo 07:56
07:46 ex Guildford 07:22 all to Surbiton then Waterloo 08:17
07:53 ex P& Southsea 06:10 Walton, Esher, Surb, Waterloo 08:22
08:00 ex Farnham 07:27 all stn to Surbiton, then Waterloo 08:31
08:16 ex Bentley 07:33 all stn to Surbiton, then Waterloo 08:47
08:24 ex Chertsey all stn to Surbiton, then Waterloo 08:54
08:31 ex Alton 07:54, Walton and Waterloo 08:57
08:46 ex Ports&S 07:08 all stn to Surb, Waterloo 09:16
So basic service was half hourly, in 30 mins from Weybridge with peak extras. Some peak hour trains took 31 minutes. SWR is embarrassingly slow compared to post war Southern
The train starting at Chertsey doesn't appear to be via Virginia Water.