some years ago i did some thinking on that find-the-odd-ball-in-3-measurings-problem. hope you know that one. well, outcome of that was, that in 3 measuring you can find an odd ball out of 3^0 + 3^1 + 3^2 = 13 balls. in 4 measuring you can find one odd ball in a total of 13 + 3^3 = 40 balls.
now, back to the point. for some reason that is unknown to me, those numbers work here too.
3^0 = 1 kg
3^1 = 3 kg
3^2 = 9 kg
3^3 = 27 kg
with those 4 numbers/weights you can express all numbers up to 40 using only + and -
now big question: how many weights do you need to weigh any number between 1 and 364 kg?
edit: technically, all you have to do is start with 1 kg. then add up all weights you have, multiply by 2 and add 1. thats the number for the next weight. makes sense, doesnt it?