If he lived in Germany, his name would indeed have the "eye" pronunciation but in the United States both the "eye" and "ee" pronunciations show up for this name, for reasons having to do with ethnicity, sound drift, and chance. There is a German name Weiner that comes from a dialectal pronunciation of Wagner, related to Waggoner, meaning wagon-maker. But Anthony Weiner is Jewish, and according to dictionaries of Jewish surnames, his name probably originates from the Yiddish name Vayner, meaning wine merchant. Yiddish is related to German, and Vayner is related to the German word Wein for "wine," and pronounced with the "eye" vowel. But there is another less common but also predominately Jewish surname Wiener, meaning someone who comes from Vienna.
