You can get digital postal scales at Staples, Office Max, or any good office supply store (or online) for under $20. Most weigh up to 15 or 20 pounds, have a tare function, and measure in either grams or ounces/pounds. Scales that weigh down to 1/10 g are relatively inexpensive and plenty accurate for this work. Beware of cheap scales that show results in tenths of a gram but actually have an accuracy of +/- 2 or 5 g.
I have one similar to this and it does double duty as a shop and kitchen scale. I keep it clean by zipping it into a gallon Ziplock bag and changing bags between jobs. You can easily work the buttons and the bag doesn't seem to cause any change in the resulting weights.
For a whole bike or frameset, I use Interceptor's method with a bath scale accurate to +/- 25g but there are hanging fish/game scales that are pretty accurate that you could carry with you if you wanted to spot check bikes on location. Most bike shops have a scale and will weigh a bike if you ask.