With some airlines (particularly budget carriers, such as Ryanair), you're only allowed ONE piece of cabin baggage. If you've got two bags you have to squeeze one inside the other. That includes handbags, laptop cases, camera bags, etc. So your handbag would definitely be weighed (since it would either contain the rest of your hand baggage or be inside it).
If you've got several items of hand baggage it's still likely that they'll all be weighed, with the aggregate weight having to be no greater than 7Kg.
Chris