in arizona, if my mothers will was not notarized, what weight does it carry?

Wills are generally not valid unless certain formalities are met, but these formalities do not always include notarization (I don't know the specific formalities Arizona requires, but I'm sure it requires that your mother sign her will, about which your question is silent).  These formalities may have been met here, as you indicate that your brother signed the "will" as a witness.  Also, there are some circumstances (generally invoving imminent death) where many jurisdictions relax the formalities.   Also, what you characterize as a "will" does not sound like one to me, although obviously I don't know the whole story.  From the facts you set forth, the document may reflect a gift (your mother giving your brother the right to live in her home after her death) or a contract (your mother agreeing to let your brother live in the home in exchange for something he gave her or did for her, such as care for her during her life).  A gift or a contract would generally not require the same formalities to be valid as would a will.