Does basicity always vary inversely with ionic atomic radius???

Not necessarily... It's only a guideline, and one that easily gets confusing. So it's not a good guideline to try to make sense of.

We need to determine what "basicity" means. You did not specify either Lewis or Bronsted basicity, which both make a difference.

Take `"I"^(-)` and `"Cl"^(-)`, for example...

BRONSTED BASICITY

Bronsted basicity generally depends on the ability to polarize a proton's bond with another atom, weakening the bond and promoting the Bronsted base's acceptance of that proton.

When you place `"I"^(-)` and `"Cl"^(-)` in water... `"Cl"^(-)` is the stronger Bronsted base, because:

1. It is smaller, making its electron density, well, denser, making it less polarizable by another species. Thus, it is a harder base.
2. It is more electronegative, making it more polarizing towards the proton on water than `"I"^(-)` is on water.

That allows a stronger hydrogen-bonding interaction than `"I"^(-)` would have with water, which in this case makes it a stronger Bronsted base (a stronger proton acceptor).

(Indeed, we say that `"HI"` is the stronger acid, and so its conjugate base is generally stated to be a weak base.)

LEWIS BASICITY

Lewis basicity may depend on the following factors:

• electronegativity
• solvent effects (hydrogen-bonding, for example)
• strength of the conjugate acid's `"H"-"A"` bond(s), and the trade-off you get upon trying to make that bond.
• and probably other stuff.

In terms of Lewis basicity, since `"I"^(-)` is less electronegative, its valence electrons are held less tightly to the nucleus (it's a softer base).

That increases its effectiveness as a Lewis base.

http://crab.rutgers.edu/~alroche/Ch06.pdf, pg. 16

However, `"I"^(-)` is larger than `"Cl"^(-)`, so the bonds it makes are naturally weaker, which is not a great tradeoff for donating its electrons, lowering its Lewis basicity.

http://www.t.ibchem.com/

It's unclear how this all balances out without more context. So, keep in mind... context is extremely important, and defining your words is as well.