Not sure about this one...but....
We can weigh any positive integer amount up to
7 grams with weights of 1, 2 , 4 grams
15 grams with weights of 1, 2, 4, 8 grams
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.
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63 grams with weights of 1, 2, 4, 8, 16, 32 grams
127 grams with weights of 1, 2, 4, 8, 16, 32 ,64 grams
So...7 weights