Oh, Richard, Richard...

A smaller wire diameter has MORE inductance, not less, in the same
environment. Think for a moment about coax: reduce the inner
conductor diameter, and the impedance goes up while the propagation
velocity stays the same. That means that C goes down and L goes up.

For Pier something else to ponder is that the change for resonance
(zero reactance) in a half-wave dipole is considerably less than the
change in a full-wave ("anti-resonant") dipole, for the same wire
diameter change.

I don't think that simple concepts of the antenna behaving like a TEM
transmission line are going to cut it here, and I'll wait for a better
explanation than that.

Cheers,
Tom