I came across an example like this:
頼り無さげに 見られるぶん；生徒達に慕って もらえるのは 素直に嬉しい
tayorinasage ni mirareru bun; seitotachi ni shitatte moraeru no wa sunao ni ureshii
After searching several grammar dictionaries, I haven't seen a single example of ぶん used like this, nor of げ used after a さ nominalization of of an i-adj. Eventually, with the help of a native Japanese-speaker, I parsed this sentence like this:
"The degree to which I am seen as appearing unreliable, as for being able to get my students to look up to me, I am truly happy."
I've interpreted it as the teacher explaining that she'd rather be admired than respected. For a more natural translation:
"As much as they might see me as unreliable, my students' affection is what truly makes me happy."
This seems like an odd usage of ぶん, I'd expect either ほど or くらい in this position. The closest example on this site I've found is: The meaning of “ぶん” in “見ているぶんには…”, but this deals with a post-verb ぶん only in a specific context. Is this use of ぶん common?