I can't give you an average, but I have a tube of Victor Champion (speed 78) in front of me on my desk. The whole thing (with tube, shuttles and end caps) weighs 209 grams. Each shuttle weighs about 5 grams. I did this on a kitchen scales, the calibrated unit is being used at the moment.
last nite i was curious and weighed half a dozen feather (wilson classic) and nylon (mavis 500) one at a time (6 measurements) and interestingly enough they came up exactly the same the entire way through. On average each shuttle weighed a little less than 1/8 gram. My scale weighs in 1/8th