I would like to know about your family, as I don't have Benjamin or Florence Alberta Pillow. At least these dates might for now help.The State of New York issued the cards, therefore they were residents of that state during late 1936 or after (Social Security Act of 1935). If you send off for their Social Secuity Applications you will find you find a treasure chest of information - DOB, POB, Parents, etc. Look for the letter at Ancestry.com.
Also I suggest looking at the 1900, 1910, 1920 New York Census for Wieghtman Edwards. Do you know if this is a middle name or his given name?The 1930 Census will be available in April, 2002, but the search will be more difficult (http://home.att.net/~wee-monster/1930.html).
Email me for more history of the Pillow Family.
Death certificates can also be obtained.Go the the county of death -I have found mortuary records maintained by each county to be extremely helpful - it reports who reported the death, cause of death, place of death, who they were living with and where they were residing at the time of death, place of birth and parents, etc..