To what reading level does a specific word like 'verbose' belong?

There's an (old — 1971) book called the Living Word Vocabulary that gave reading levels for different words. In it, "verbose" is given a score of 12–72%, which means that on a multiple-choice test, 72% of 12th graders could identify the correct meaning of "verbose".

I don't know how to check "reading level" per se, but you can substitute for it by checking the usage frequency of individual English words online.

For instance:

• A sample of the the top 60,000 lemmas from the Corpus of Contemporary American English (COCA)
• Wiktionary Frequency lists

The assumption here being that the more common words are more likely to be known to users than rarely used words.

According to a study on vocabulary*, high school grads will know approximately 12k word families and approx 17k word families by the time they complete college.

As such, you can use as a rule of thumb that any word past the 12k mark in frequency rating can be considered to be challenging for most users. (with of course of a lot of exceptions)

Also, keep in mind that while some words are commonly used, some definitions of these words can be very rare, making them likely to be misunderstood. In my opinion, the most challenging words of the English language are small common words such as "to", "as", "in", etc. which can have 10 - 30 different definitions.

Checking frequency is a negative test: If the word is not frequently used, you can safely assume that it will stump some of your readers, but it does not guarantee that a word frequently used will be easy enough either.

This is a great question, by the way. I find that one of the most neglected areas of software documentation is the definition of terms used and what they really mean in the context of the software.

* E.B. Zechmeister, A.M. Chronis, W.L. Cull, C.A. D'Anna and N.A. Healy, Growth of a functionally important lexicon, Journal of Reading Behavior, 1995, 27(2), 201-212 (Referenced in Wikipedia's article on Vocabulary.