I have discerned these factors affecting orbital overlap:
Type of orbital
Nodes along the internuclear axis
$n$ quantum number of the atomic orbitals - the number of shells of electrons
Size of the atoms
Geometry of molecule
Angle of overlap
With respect to the binary halogen acids, I still have the following questions:
I can understand how one might argue that the binary halogen acids become more polar as one goes down group 7, in that electron density isn't very well shared; overlap is poor because of the small 1s orbital of hydrogen and the increasingly larger hybridized orbitals of the halogens. But this is half of what constitutes ionic character.
I.e. what about the electron on hydrogen? As the halogens get bigger, electronegativity decreases. How can the electron from hydrogen be isolated toward the halogen as EN decreases?