The wing on the B744 were redesigned totally by Boeing to be made of different materials and have different aerodynamic performance over the 747 classics. It was not simply a case of adding wingtips to the old 747 wing. In doing this, Boeing delibarately altered the angle of the chord line at the ends of the wings. This was designed to reduce wingtip vortecies and make the wing more efficient. It has an added effect of reducing the likeliness of 'dutch roll'.
The wings may flex and droop due to fuel, but the downward angle at the tips is a design feature.
I don't have any more info, but i'm sure if you try the Tech ops page someone will help out. Most likely even correct the above!
(and feel free to, i only rememebr reading the above somewhere and am no expert!)