In conversation today I was struck (it left a bruise) by this peculiar item. Growing up in Philadelphia I realize a part of my regular speech pattern includes reference to the past as, "used to be". We also say, "I was used to..." meaning 'accustomed'.
There are many oddities in our language that I can deduce the origin.
This one is a puzzle to me!

Can anyone illustrate the root of such an odd collection of words? Analyzing the phrase (and I can imagine someone for whom English is not a native language having a question) it makes no sense. These words simply don't work together.

I am very interested in your thoughts.

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That's an interesting question. It's right up there with why we use "have" to indicate perfect tenses or "go" as a periphrastic future. The latter is commonly used in Romance languages, but only, as far as I know, in English among the Germanic languages.

Well, thank you for the response.