Solution:

An element $x$ is the greater element of a two-element subset exactly once for each smaller element of the set, so $x$ contributes to the sum once per element below it. Sorting the set as $1, 2, 3, 5, 8, 13, 21, 34,$ the sum of the list is $$0(1) + 1(2) + 2(3) + 3(5) + 4(8) + 5(13) + 6(21) + 7(34) = 2 + 6 + 15 + 32 + 65 + 126 + 238 = 484.$$