Cooking something like meatballs follows a similar pattern as diffusion. As such, cooking a large slab of meat (or anything) n times thicker will take n^2 cooking time.
However a sphere is a slightly special case because it is far more like heating one end of a cone than both ends of a regular prism.
This leads to the spherical object cooking faster than a slab, but the relationship is still the same.
However, if you cook the meatball in a frying pan, you are using a temperature high enough to cause a maillard reaction on the outside. If you cook them at this temperature for too long (i.e. to cook a larger meatball) then you will burn the outside.
To cook larger meatballs you need to use a lower temperature for longer, and then finish (or start) with a high temperature to brown the outside.
The ideal method would be to sous vide them (perhaps for a couple of hours -- up to 4 -- at 60C) before frying them to get the nice surface texture and flavour.
The traditional method of cooking the meatballs in a sauce does a similar thing.
So, if you're cooking them in sauce (say for 30 minutes) and you make a meatball twice the diameter, then brown them, and simmer for 2 hours.
See
here, and
here, and finally
here.
