I've only ever seen bags weighed at security or boarding pass checks prior to going airside. I had heard that having scales at boarding gates is tricky as they have to be externally checked to ensure they comply with regulations.
After flying out of STN in January my handluggage wasn't weighed anywhere, not even the bag drop desk.
Although some people are caught out (for not following very specific instructions outlined on the website, on the boarding pass and also emailed to you around 7 days before departure - an email sent just about hand luggage regulations outlining size, weight and that you will be charged if it doesn't comply) I have noticed a massive improvement with hand luggage. People are learning to comply, gate staff are getting better and delays due to oversized luggage have massively reduced.