LHR is like that 99% of the time when we used SK after our UA TATL, they announced that all hand luggage would be checked in for free.

@OP whether they weigh your bag is highly based on what impression you give the gate agents: if you are carrying a sink (someone said they saw people carrying a sink onto a UA flight) or a suitcase that "looks" heavy (when you move it) or you have a duffel bag that looks huge, of course they will ask your bag looks bulky. As long as you use a carry on suitcase that may be slightly bigger than allowed and you keep your laptop and accessories in a separate bag as they are counted as things that are on top of personal items. (at least that how UA defines it). If you have a backpack that fits a laptop and you put all those things in there, if they complain you tell them that it is your laptop.