Here is the sentence:
He was not accustomed to being made light of.
What does "to being made light of" mean?
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You might rather want to change your question title to "What does 'make light of' mean?"
"to being" is related to the verb "accustom" as in the following examples:
I'm not accustomed to this tropical weather.
He's still not accustomed to his new environment, i.e. to being mocked all the time.
Finally according to the definition of "make light of" that CipherBot has put, the rephrasing of your sentence would be:
He is not used to being treated as unimportant.
In other words,
He has always been treated respectfully or importantly, but now his circumstances have changed where many people don't regard him as important as he thinks he deserves.
Made light of definition, #37
Make light of, to treat as unimportant or trivial:
They made light of our hard-won victory.