After passing through a central security search-point, random spot checks are sometimes carried out on entry to the boarding gate waiting rooms. But they're not interested in the weight, only what's in your bag.
The purpose of the weight restriction is largely to do with preventing injury to others should your bag fall from the overhead locker. But there's no weight restriction on goods bought in duty free. You could buy a 40kg crystal vase in duty free and walk on board with it!
Some airports are now doing away with those centralised security search-points that all passengers have to pass through. It's been realised that these produce the chaotic queues seen at, e.g., Heathrow. Instead, security search-points are being set up at the entrance to individual gate waiting rooms, so fewer people need pass through at any one time.
At such airports, your duty free will be put in fully sealed clear plastic bags on purchase.