Indeed dgreening, I understand the problem the same way as you do. If you need to know the exact weight of a regular coin, you need a supplementary weighing. I think also about a balance with two scales, that only tells you whether what is in the left scale is heavier or lighter than what is in the right scale.
my sincere apologies..i tried to edit the info about the 1unit weight when i realized its too late..The puzzle was originally for the balance scale..but the solution for the classic odd out of 12 in 3 is applicable so i shifted to such weighing scale..With unknown unit of each, the puzzle would look like a simple problem as presented by phil..thanks all for your interest