I have a Pashley Princess Sovereign, 20" frame. It is a heavy bike compared to contemporary road and mountain bikes, but it is lighter than the Dutch transport bikes including Azor and Gazelle.
When it comes to bikes of this kind, the weight is there for a reason. It will help you when it comes to stability, smoothness when riding over potholes, and in bad weather conditions, including winter cycling. The weight is actually good for cycling against the wind, because it allows the bike to resist it. As far as gearing goes, any upright bike will require more leg strength to pedal; just ask your local shops to set the gears lower.
The only problems that I have due to the weight of my Pashley have to do with lifting it. I am a slim, out-of-shape female, and could not pick up the Pashley in order to carry it down the porch stairs when I first got her. However, after 2-3 days, I developed enough arm strength to do it successfully, and it is no longer a problem.
Some posts about my Pashley:
http://lovelybike.blogspot.com/2009/...-was-made.html
http://lovelybike.blogspot.com/2009/...r-cycling.html
http://lovelybike.blogspot.com/2009/...nd-basket.html
http://lovelybike.blogspot.com/2009/...spectator.html
Hope this helps!