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Down the group, atoms of the alkali metals increase in both atomic and ionic radii, due to the addition of electron shells. This results in the charge density of their corresponding cations decreasing down the group. Thus, as we go down the group, the cations become "softer".
Now, note that the hydride ion is "hard", having high negative charge density. While the carbonate ion is "soft", having a lower negative charge density.
Applying the "hard-soft acid base" (HSAB) principle, we would expect the "hard" ions to form more stable compounds with each other and the "soft" ions to form more stable compounds with each other.
Since the heavier alkali metal ions are softer, we would expect them to form more stable compounds with carbonate. As for the harder lighter metal ions, we would expect them to form more stable compounds with hydrides.
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