I've never encountered a question like that. I'm thinking though, that you could reach a rough approximation on an excurrent tree like a spruce, by using the height of the tree, and the radius at the base, to calculate volume as though it were a cylinder. (Height x pi) x (radius squared) The stem of the tree of course is not cylindrical in shape, but in a rough approximation the excess volume that you'd get as a result of calculating it as a cylinder, rather than as a cone, would be offset by the weight of the branches.
Once you had the volume calculation, you could then convert it to cubic feet and use a green log weight chart.
Perhaps you could try testing the calculation on Sitka specimens small enough to weigh, to see how it works out. Small spruce seem proportional to larger specimens.
I also found a page with algorithms for calculating tree weight. You can view them here.
http://www.shodor.org/succeedhi/succeedhi/weightree/math1.html
The algorithms are taken from "Tables for Estimating Total Tree and Product Weight and Volume of Major Southern Tree Species and Species Groups" Joseph Saucier and Alexander Clark III , Southwide Energy Committee, American Pulpwood Association Inc., Nov. 1985.