The Eve Of Results

So... I get the results of the 2nd course at the college today, namely "Foundation Area Control Service" but we just call it "Foundation". I say today but between me and them there's some sleep to be had, it's a bit late in the evening. I can happily say that I've done well. I may or may not have explained the marking system before but I passed all 5 sections in all 6 exams so that should mean a guaranteed Satisfactory as the instructors say... Meanwhile I have a problem about which I have been pondering. I remember hearing the problem first posed to me back by a Maths teacher when I was only eleven and it goes like this:

In a conventional set of weighing scales in which one adds a sum of weights to one side and food to another to balance the scales one requires 9 weights to accurately weigh up to 350g in 1 gram increments, namely 1g, 2g, 4g, 8g, 16g, 32g, 64g, 128g and 256g. So to weigh 30g one balances the combination of weights of the 16g + 8g + 4g + 2g = 30g, or for 101g one adds the combination of the 64g + 32g + 4g + 1g = 101g.

However what if you could add weights to both sides not just one as normal? For example to weigh 10g of salt:- on the side with the salt one could have a 70g weight a 50g weight; adding a 130g weight to the other side would balance the scales ie, 10g of salt + 70g + 50g balances 130g. Using this system would one need fewer weights to weigh up to 350g? How many would one need? and what size would they be (clue not necessarily 70, 50 and 130)?

As I'm on holiday this week in the Alps please submit your answers in the comments section of this post and I shall post the answer when I get home.