When I travelled through Stansted (May 2010) they had plenty of scales dotted all around the terminal
Only problem was that you had to pay to use them. It also wasn’t a case of having a set amount of time to weigh the luggage, but one suitcase per payment
In the end I bought myself some of those handy little luggage scales that seem to be accurate enough to do the job (which can also be put in your hand luggage for the return trip). End of problem