We investigate the formation of polymer vesicles, or polymersomes, of polystyrene-block-poly(ethylene oxide) diblock copolymers using double emulsion droplets of controlled architecture as templates. To engineer the structure of the polymersomes, it is important to consider the concentration of diblock copolymer in the middle phase of the double emulsion. We describe how the presence of excess polymer can induce a transition from complete wetting to partial wetting of the middle phase, resulting in polymer shells with inhomogeneous thicknesses.