Re: Anton W. (Anthony) WEIMERS- PA and NY
PA under naturalization on the census means First Papers, not that the person was naturalized in Pennsylvania. In all likelihood he was naturalized in NYC. I suggest trying to get a copy of the record.
You might also try to get a copy of Anton and Rose's marriage record. It may indicate what happened to Anthony's first marriage.
You might try to get Anton's obituary and death certificate which in a city the size of NYC may not be easy.
Sorry I don't know where in NYC you go to get such records but I'm sure the NYC Library or the local historical society can help you.