I think Sigourney was the second actress to do that, & I remember that last year Jamie Foxx became the first actor to do it. But of course he won in the Leading category.
Jessica Lange (Frances and Tootsie) was another. There are more, I think... generally if you're nommed for both you win one or the other. Sigourney's one of the few who lost both.
Lange is the other one I was thinking of, and you're right, there were two others. In 1938 (Fay Bainter) & 1942 (Teresa Wright). In both cases they won in the Supporting category and their co-star in that same film defeated them in the Leading category. But those were some legendary performances they lost to: Bette Davis in
Jezebel & Greer Garson in
Mrs. Minniver. So Weaver was the only double-nominee to lose both chances.
Glad you made me look that up.