Solubility of Noble Gases
Wikipedia gives the following solubilities for the noble gases in water at $25^\circ \text C$ in $\mathrm{cm^3~kg^{-1}}$:

$\mathrm{He: 8.61~~~Ne: 10.5~~~ Ar: 33.6~~~ Kr: 59.4 ~~~Xe: 108.1 ~~~Rn: 230}$

Why does solubility of noble gases increase down the group?

The intermolecular interactions of noble gases are in the form of London dispersion forces, which are strongly influenced by the polarizability of the atom which increases as the atomic radius increases. This can be thought of as resulting from the electrons being 'less tightly bound' to the nucleus and the atomic radius increases. Atomic radius increases down the group therefore solubility also increases. For more on polarizability see here.

Why is radon not the most soluble noble gas?

Radon (and other heavy radioactive elements) are often ignored when talking about trends because they are uncommon. Radon is in fact the most soluble noble gas but the half lives of its isotopes are on the order of hours or days so it is not really very useful.