I've been married six weeks and I've made a big mistake. He won't work, he says he's "retired". He told me he would work with me at my business before we got married. Can I have this annulled?

You can try, it will depend on the state laws, you may have to divorce.

Was he working at your business before? Not tell you, I would assume you dated for months or more, so while dating and engaged did he not work with you?

If not, why did you expect him to change his ways.

It really depends on the state you are in. The length of time isn't really important, it's the reason for the annulment. States have different rules as to the reason for filing for an annulment. Some states allow mental illness, incest, etc.
You'll need to find out your state laws to determine if this marriage qualifies for an annulment. Annulments are usually a bit more difficult, why not just file for divorce and get it done & over with?
Best of luck,

Where do you live? Our answers will be different depending on what area of the world you live in.