Depends how you define weight.

http://en.wikipedia.org/wiki/Weight

There is also a rival tradition within Newtonian physics and engineering which sees weight as that which is measured when one uses scales. There the weight is a measure of the magnitude of the reaction force exerted on a body. Typically, in measuring someone's weight, the person is placed on scales at rest with respect to the earth but the definition can be extended to other states of motion. Thus in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless.