This paper details the design, the implementation, and the experimental verification of a minimum weight input series output parallel (ISOP) structured Dual Active Bridge (DAB) converter for an Airborne Wind Turbine (AWT) system. The main power components of the DAB converter, in particular the bridge circuits, the actively cooled high frequency (HF) transformer and inductor, and the cooling system, which largely contribute to the total system weight, are designed and realized based on multi-objective considerations, i.e. with respect to weight and efficiency. Furthermore, the design includes all necessary considerations to realize a fully functional prototype, i.e. it also considers the auxiliary supply, the control for stable operation of the system, which also comprises an input filter, over the specified operating range, and the startup and shut down procedure. These considerations show the complex interactions of the various system parts and reveal that a comprehensive conceptualization is necessary to arrive at a reliable minimum weight design. Experimental results validate the proposed design procedure for a realized lightweight DAB hardware prototype with a rated power of 6.25 kW. The prototype weighs 1.46 kg, i.e. features a power to weight ratio of 4.28 kW/kg (1.94 kW/lb), and achieves a maximum full-load efficiency of 97.5 %.