Drag is the main impediment to fuel mileage, but you probably won't see a whole lot of difference in an "aero" design versus a boxier one for a similar size trailer. Maybe 1 mpg. Maybe. That's because the frontal area is huge regardless of how aero the shape is, so there is still major drag. 60 sq ft of frontal area is still 60 sq ft even if the corners are rounded and the roof sloped. The only way to really beat the frontal area drag is to reduce the height, e.g. with some sort of fold-down trailer, and thus reduce the sq ft of frontal area substantially.
Weight does matter for mpg, but mostly only when accelerating or climbing hills. A larger, heavier trailer has to have larger tires, and the tires carry more weight, both of which increase the rolling resistance of the tire. However, the rolling resistance of a properly inflated tire is small, so a slight increase has only a small effect.