I'm sure Scott Black has this all figured out but it would seem that Bix inadvertantly had the name associations reversed. By that I mean Weiss was Alice's -father's- name and O'Connell was her -mother's- maiden name. The following "informed speculation" comes from U.S. Census records:
Alice Weiss, daughter of Theodore Weiss and Nellie O'Connell, was born about 1908 in NY. Theodore, born 1869 in Germany, worked as a waiter in Manhattan. Nellie was born 1876 in Ireland. Nellie's father Phillip O'Connell lived in the household in 1900. Theodore and Nellie had a large family so it's quite likely that there are descendants who could shed more light on Alice. By 1920 Theodore Weiss had died and Nellie Weiss' family included Alice and youngest daughter Vera.
By 1930 Alice Gavitte (yes), married, age 20 [sic], and her younger sister Vera Weiss, single, age 17, were living at 24-60 32nd St., Astoria, Queens. This was Rex Gavitte's home address.
No Helen Weiss was found among the family that may be Alice's, so indeed if they are distinct individuals they may be cousins. Or, maybe Helen was a pet name for Vera Weiss. Or...this line of research is totally wrong!
1900 US Census, Manhattan, T623 roll 1114, pg. 116
1910 US Census, Manhattan, Ward 12, T624 roll 1014, pg. 107
1920 US Census, Manhattan, T625 roll 1219, pg. 129
1930 US Census, Queens, T626 roll 1583, pg. 57
Possible death info:
Theodore Weiss died 22 Sep. 1916 in Manhattan, age 47, (cert. 27528)
Nellie Weiss died 16 Mar. 1925 in Manhattan, age 49 (cert. 7624)