It's actually the listeners who write 'SWs to you' (rather than Sarah re-writing the text of their letters).
As others have indicated, many listeners noted that Steve Wright only ever seems to read out letters and emails which include things like "Great show, Steve. You're the best thing on radio". (i.e. Steve Wright's ego is about the same size as Jonathan Ross's vanity, Chris Evans' bank balance and Terry Wogan's holiday entitlement - Massive!). After this was mentioned by Sarah Kennedy, listeners started to write to her and adding "Steve Wrights to you". This soon got shortened to 'SWs to you'.
Sarah's broadcasts often seem to need a translator for the uninitiated. Her frequent absences are nearly always attributed to problems with her 'chesticles'. Someone with a badly tuned radio could easily wonder if she was really female ;-)
Chris