I am using version 0.79.064 of aacenc32.exe and version 3.2.0.18 of aacenc32.dll. Whether or not I include the switch "-profile LC" in the command line when I make a file, aacenc32 reports "AAC profile: LC" when making the file. But, the number of bits in the resulting file is not the same. I get a slightly larger file when I explcitly include "-profile LC" than when I do not.
You might be asking, "what does 'LC' mean?" LC stands for low complexity and it is how AAC is usually encoded. However, there is a "Main" profile in the AAC standard that includes backwards prediction in the encoding scheme (source: Wikipedia).
But I don't know what is really happening here.
Neither the Nero User Manual nor the application itself are any help. It's kind of disappointing that the Nero dll has all these switches available in it but the Nero GUI doesn't give you access to any of them.

Your problem doesn't seem to have anything to do with the Nero encoder or the Nero GUI itself, but rather some weird issue in an unofficial, unsupported frontend.

Does this tool perhaps spam the encoding options into the file? In that case, it would explain why the file gets a tiny bit bigger, since you used an extra option.

It turns out there isn't a problem after all - for some reason Windows Explorer didn't update the size of one of the files even though I had recorded another file in the exact same directory whose size did get updated. Oh, well.