Actually The Imperial State Crown is relatively light (at 4lbs) as it's frame is Platinum.
St Edward's Crown (the one used to actually crown a Sovereign) weighs in at 8lbs;as it's nearly pure gold,,so heavy for a King and worse for the Queen in 1953.
I don't know how they get the Imperial State Crown to and from the Tower,but here is a little story.
One of my Daughters used to work for Garrard's (The Crown Jewellers) in Regent Street.
She worked in the same workshop as the guy who held the title "Crown Jeweller".That is he was responsible for the cleaning/maintenance of all the Crown Jewels.
When he was due to clean the Imperial State Crown (usually before the opening of Parliament) he went to the Tower,dismantled it (all the Crown Jewels can be disassembled) put in his capacious (old fashioned) briefcase and carried it on the tube back to Regent Street.
Securicor carried what they thopught was the crown,and any robber making an attempt would probably have targetted their van.
Of course in reality these Crowns etc and the large diamonds etc they contain could neber be sold,although they might disappear into some "Black Museum" somewhere.
He used to take great delight in shocking my daughter by showing her the crown in his briefcase,but he never let her try it on where complete again!
Spoilsport.
BTW,if you don't know what a "Black Museum" is let me know if you are interested.