Just to explain my thinking a little more rigorously (and consistent with DeltaT's attachment), it's true that any weight added to the wing, considered by itself, creates a downward bending moment about the wing root. But if you think about it, weight added to the fuselage, considered by itself, creates only a downward force on the fuselage and has no effect on wing bending.
But any weight added anywhere on the aircraft (assuming level flight, symmetrical loading, etc) requires an equal increase in lift. The increase in lift acts through the center of lift on each wing and (considered by itself) creates an increase in upward bending moment about the wing root.
If the the weight is added to the fuselage, the upward bending caused by the additional lift is the end of the story. But if it's added to the wing, the the downward force from the weight must be considered.
If the weight is added inboard of the center of lift, it acts on a shorter moment arm than the lift, and partially offsets the upward moment. The net result is an increase in bending moment about the wing root, but smaller than if the additional weight were in the fuselage. Weight added at the center of lift acts on the same moment arm, and exactly offsets the upward bending from the lift. And weight added outboard of the center of lift acts on a longer arm and more than offsets the upward moment from the added lift, resulting in a net decrease in upward bending moment.