Weybridge really is part of London.. good trains into the centre (Waterloo Station..) use this App (on laptopn and iPhone/ Andriod to find out abou travel arrangements... its really good.
Trains into town take c30-40 mins and once into Waterloo everything is close by.
If you do fancy it let me know and we can meet for a beer!...
If you have some time and don't fancy travelling then go visit Brooklands Museum...
Brooklands Museum
Place to go if you love cars... and planes ..
Great museum and now home of AC cars and they make Cobras there!..