As stated elsewhere, weight and balance are important in a plane, and accidents have happened as a result. I've taken a number of small plane commuter flights in the US and they regularly asked how much I weighed, and they definitely weighed my baggage. The smaller the plane is, the more it matters.
Safety is one aspect, efficiency is another- knowing how much you weigh also tells the airline how much fuel they must put on board, and even how much cargo they can safely take- much cargo flies on a space (weight) available basis.
Hell yeah, I want them to know how much weight is on the plane.