I have seen a lot of citizenship problems in police papers found in the Czech National Archives. It seems it was a tricky situation.
Austro-Hungarian citizenship based on "home rights" in a certain community. The Austrian law -- No. 103 from December 1863 -- stated that a woman lost her original home rights and took on those of the husband with marriage. That explains the situation of Mr. Resnicoff's grandparents. Conversely, the U.S. probably did not automatically issue citizenship to the wife just because she married a U.S. citizen. According to the Austrian Law No. 105 of 3 December 1863, paragraph 19, on which Czechoslovak law later based, Mr. Weinberger should have been designated as having "home rights" in the place of his birth after becoming homeless due to his father's emigration. Why that didn't happen, I don't know. Unless it had to do with the change with the break-up of Austiria-Hungary in 1918.
In the 1920 Czechoslovak citizenship law, ethnically non-Czech and non-Slovak people with home rights on the territory of what became Czechoslovakia were supposed to opt for Czechoslovak or another/their former citizenship. If they failed to do so, then they could became stateless.
However, statelessness was only really problematic when it came time to travel outside the country. In day to day life, it made little difference. If Mr. Weinberger did not opt, then it was not a great problem in a practical sense during the Republic. All of that became a nasty problem, however, after the Sudetenland crisis, and I've seen many examples of the Czechoslovak authorities acting arbitrarily to the detriment of non ethnically Czech/Slovak, especially German-speaking people/citizens and Jews in that period (Sept. 1938-March 1939). Many Jews with Czechoslovak citizenship fled the Sudeten region in peril of their lives with the Nazi takeover and the central authorities were very reluctant to allow them in or to allow them to stay.
That became worse after March 1939 with the Nazi invasion. Whoever didn't have their papers in order and didn't get out somehow very soon, by May, June 1939 could be in real trouble. The bureaucratic hurdles made it almost impossible, and many ended up in the camps and murdered for that very reason.
Rick Pinard, Prague