Why are the ozonides of heavier elements more stable?
Potassium and heavier alkali metals ozonides are formed by treating with ozone, or by treating the alkali metal hydroxide with ozone. They are very sensitive explosives that have to be handled at low temperatures in an atmosphere consisting of an inert gas. 

Lithium and sodium ozonide are extremely unstable and must be prepared by low-temperature ion exchange starting from $\ce{CsO3}$. Sodium ozonide, $\ce{NaO3}$, which is prone to decomposition into $\ce{NaOH}$ and $\ce{NaO2}$, was previously thought to be impossible to obtain in pure form. However, with the help of cryptands and methylamine, pure $\ce{NaO3}$ may be obtained as red crystals isostructural to $\ce{NaNO2}$.

As pointed out by user2617804, lithium and sodium ozonide are extremely unstable because the ozonide ion is big for the tiny sodium and lithium ions so it is stretched around it due the distributed charge on the ozonide ion- puts it under large internal stresses.

See wikipedia for more details.