What is the minimum number of weights which enable us to weigh any integer number of grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only on the left pan)

The minimum is $7$ weights. Six weights yield at most $2^6-1=63$ nonempty left-pan selections, while the seven weights $1,2,4,8,16,32,64$ represent every integer from $1$ to $127$ in binary. Five powers-of-three weights would rely on allowing weights on both pans.