And THIS is where the smaller diatonic box really shines. It's easily possible to throw them overhand, with good form, and high velocity. Sure, the big PAs and CBAs hit hard, when they hit at all...
If we get serious about accordions, and not just type random jokes about throwing them, then one can see several areas for accordion development.
1) Walker has already mentioned the technique - I agree it is vital for a good result, and if double straps are allowed, then a "hammer turn" must be one of the best ways to draw inspiration from, regardless of whether it's a PA, CBA or diatonic.
2) It's not just about weight, it is about the ballistic coefficient, which is calculated as:
BC=mass/(drag*cross-sectional area)
You will get better results if the squeezebox flies in a straighter line, and the mass per cross sectional area is maximised. Big yes to double-cassotto boxes and slick aerodynamic curved grilles like a Hohner Morino. Big no to the square Steirische boxes with random stuff sticking out of the casework, generating more drag. Concertinas are too light to go far, and bandoneons are probably the worst, as they are square and have a very large cross-section to weight ratio.
In case we are not going just for distance, or distance & accuracy (like golf for instance), there has to be some weight in the box, otherwise it will get blown off course by sidewind, or, with a very strong headwind it might actually boomerang back into its owner's face.