I like the overkill of MrMike's spreadsheet, however, I think we can simplify this down if I did my algebra right.

Cg (forward of the main gear axle) = Gear separation (NG axle to MG axle) X Weight on NG / Total airplane weight

Think that tells you where the actual Cg is in front of the main gear. Additional arithmetic to use other reference points.

What you really want to do is set the Cg to the correct location. So if you change the above around you can figure the weight required on the nose gear to set the Cg. Take the plans and measure the Cg location relative to the main gear axles. Weigh the entire airplane accurately (any method). Then level the plane with the nose gear on the scale. Adjust objects in aircraft until weight on nose gear is:

Weight on NG = Cg distance x total airplane weight / Gear separation

If you don't have any plans as might be common with many jets, you may have to do additional measurements to get the right numbers. All I need now is a nice digital scale.