Why does a bird's size effect the amount of flex in it's wings?
Well, it's to do with air resistance and how it works against the birds forward momentum. If you're a big and therefore heavier bird, air resistance effects you much less than if you are a smaller and lighter bird. Smaller birds also have a tendency to fly faster too which also increases the effect of air resistance.
We find evidence for this increased effect in birds' body profiles. In this diagram of different sized birds body shapes we can see large birds are allowed a greater range of shapes and many include what seem like aerodynamic inefficiencies such as long necks and dragging legs. Small birds' body shapes tend toward a tear-drop profile; a shape which minimises air resistance in flight.
This diagram is primarily about the different vortex gaits birds produce - a more flexed wing creates a ring vortex while a less flexed wing creates a continuous vortex. This does not really concern us but there is some interesting information in part B of this diagram. The first image shows the wing path of a smaller bird which flexes it's wing fully on the up-stroke, we can see the various vectors (forces) that are produced by the down-stroke - the lift and propulsion of the wing, the drag caused by air resistance and the overall result which lies between these. The up-stroke has no vectors, which indicates that when a wing is fully flexed no drag acts upon it. Interesting, the image below this one shows a partially flexed wing's path during flight, the down-stroke is the same but the up-stroke shows the wing will have a greater drag force act upon it however, it will also continue to produce upward, lift vectors.
This is important, we can see that the amount of bend in a wing is essentially a trade off between extra lift given by a partially flexed upstroke and the reduced air resistance of a fully flexed wing. Bigger birds flex their wings less because they are less effected by air resistance and benefit from the extra lift provided by the up-stroke, while for smaller birds it's more efficient to fully flex their wings and avoid the drag they produce.