LGKBH Here is the reply from shapeways:
Thanks for writing in.
If you know the volume of the model you should be able to calculate the weight of the model however we don't have a scheme for that.
Perhaps you can find that on the internet or perhaps someone on our forum knows where to find this information:
I do hope this helps you further.
Customer Service Agent
LGKBH Good question I guess the weight can only be answered by the printer. I'll check with shapeways to see if I can get answer.