Many excellent comments in this thread. Nick Rowe was the first to post a correct solution. Take one bottle from the first machine, two bottles from the second, three from the third and so forth. If the weight on the scale is off from the expected total by say 6 oz then you know machine 6 is the culprit. Note that this procedure will work whether the machine is putting in 1 oz too much or 1 oz too little – but not, of course, if it randomizes. (I tried to make clear the machine was always doing one or the other but perhaps this could be worded even better.)

In one of his books on lateral thinking, de Bono talks about the student who when asked how would you use a barometer to measure the height of a building said he would take it to the top of the building, drop it off, time it till it hit the bottom and then use Newton's laws to calculate the height. The student's teacher was not amused but de Bono thought this was great. In anycase, Alex J offers a similarly clever and lateral solution this puzzle which I believe also works.