UPDATED POST: The New AR 600-9 came out in June 2013. It specifically addresses calibrating scales: Here is what is says:Requires weight scale calibration annually (para B-2b).
Great question. To the best of my knowledge there is no such requirement.
Unfortunately the only information AR 600-9 provides about a scale is:
AR 600-9 B-2b:The weight will be measured with the Soldier in a standard PT uniform (gym shorts and T-shirt). Shoes will not be worn. The measurement will be made on scales available in units and recorded to the nearest pound with the following guidelines: (1) If the weight fraction of the Soldier is less than 1⁄2 pound, round down to the nearest pound. (2) If the weight fraction of the Soldier is 1⁄2 pound or greater, round up to the next whole pound.
While most active units have the standard balancing scales, there are times when these scales are not present. Therefore it is extremely important that any scale you use be calibrated. Some scales will work fine at say the 50- 100 range and then vary in tolerance as weight increases.