Hmm never computed that, actually.
Well the average damage of a d6 is
sum(range(1,6))/6 = 3.5
The average damage of a d6 with advantage is
sum((range(1,6)lambda(n)((2*n-1)*n)))/(6*6) =
(1*1+3*2+5*3+7*4+9*5+11*6) / 36 =
161 / 36 =
4.472222...
So yeah, you're right, its not actually that much.