The lightest wheeled bags I have come across are 1.5-3kgs when empty, so there goes a lot of the cabin baggage allowance weight even before transporting anything but just the bag.

An empty heavy duty plastic bag — sort of like what is used to pack in garden waste at times — weighs less and has the benefit of being a bit more weather resistant in the short term than cloth bags of a comparable size. Perhaps Finnair can handout plastic bags for cabin baggage and call it carbon neutral by saying the cabin baggage crackdown reduces consumption of petroleum products more than the fancy plastic bags consume.