Heh. That felt wrong to me as well, until I started peeving about it on this very site, and promptly got called to order by a linguist, and rightfully so.
Anyhow, see Wikipedia:
While any more is typically a negative/interrogative polarity item used in negative, interrogative, or hypothetical contexts, speakers of some dialects of English use it in positive or affirmative contexts, with a meaning similar to nowadays or from now on.
Positive anymore occurs in North American English, especially in the Midlands variety spoken in parts of Pennsylvania, Ohio, Indiana, Illinois, Kansas, and Missouri; its usage extends to Utah and some other western US states. [It] also occurs in parts of Ireland and Northern Ireland.
It goes on to list examples of usage as found in Wisconsin, Ontario, Pennsylvania, and Northern Ireland, dating back all the way to 1898.
Wiktionary marks the positive any more as colloquial, chiefly Northern Ireland, US.
Lastly, Merriam-Webster has the following usage discussion:
In many regions of the United States the use of anymore in sense ["at the present time, now"] is quite common in positive constructions, especially in speech <everybody's cool anymore — Bill White> <every time we leave the house anymore, I play a game called “Stump the Housebreaker” — Erma Bombeck>. The positive use appears to have been of Midland origin, but it is now reported to be widespread in all speech areas of the United States except New England.
That isn't double-negation, that's single negation. Double-negation would be this:
That book does not have no pages.
Sentences like the above are correct in many languages and are used in many non-standard forms of English, but are not correct in standard English.
You may be confused by the word any, which is a negative polarity item. The word any is not itself a negative, but it is required in place of no or some when the main verb is negative.
Best Answer
The best way* to negate the construction, used to be, is to simply use never and replace the infinitive form of the verb with its past tense. Thus:
It is also correct in some situations to say never used to:
In this case, never used to usually serves as an emphatic negation of something previously stated.
Your example, I used to be, is best negated as I never was/I was never, although, I never used to be and I didn't use to be (grates on my ears!) are also options, depending on the context. For instance:
Also consider the following:
Another similar set of examples:
You should always be able to determine the correct negation to use, as long you keep the definition of used to in mind:
I didn't used to is strictly ungrammatical, though widely used informally or colloquially. (The correct form is didn't use to, although this is also very informal.) Using the past tense of another verb after didn't, in this case used, is grammatically incorrect. Consider this and other similar verb constructions:
Now, the problem with these examples can be rectified by converting the past tense to the infinitive:
Also, did not/didn't always precedes the infinitive form of the verb it helps:
Here is a note from NOAD to back me up:
*(in my opinion, that is)