Yes, they weigh them, and strictly, too.
It always amuses me in European airports in winter to see lots of very "bulky" people queueing up to check in, always wearing hiking boots. Savvy folks tend to put their clothes on in layers until after the bag is weighed and tagged, and then once they get past the weigh-in, they head to the restroom, strip a lot of it off and put it in the bag.
You also tend to see folks standing in that line with puffed out pockets from various charger wires; small, but the power bricks are heavy.