FWIW: I've also tried using createFont() from within the source code, with the same results.

Yes, you guessed wrong, it is better to read the section descriptions to avoid guessing...
Also the Forum Guidelines can be of interest.

You are not the first one to have this problem (of font!), somebody guessed that createFont works better with TrueType fonts (.ttf) than with OpenType fonts (.otf). I guess your font is of the latter category, I think the concept of "several weights" is associated with OTF.

Thanks! (And sorry for misplacing the post-- I didn't see any section descriptions, just a dropdown menu with the names of the sections!)

I'm actually having a hard time figuring out what type of font my Avenir is, exactly. It's been many years since I bought it. (What's more, I was working mainly on a Windows box at the time, and now I'm on OS X.)

Avenir shows up in my Fonts folder as a directory containing a bunch of files named things like "AveniBla", "AveniMed", etc.  But the files have no extensions--neither .ttf nor .otf, nothing at all! If I select the file's icon and Get Info, OS X tells me it's a "PostScript Type 1 outline font".

I'm just adding this info in case anyone in the community here has had/solved a similar problem.  I'll try hunting around for tools to convert this into .ttf, and if I find a solution, I'll post it here.