The prizegiving, which fetes the best of the city's theatre scene, included wins for Blanchett and Weaving for their roles in the Sydney Theatre Company's touring production of Anton Chekhov's Uncle Vanya.
The Elizabeth star took home the Outstanding Lead Actress award in the international category, while Weaving was named Outstanding Supporting Performer.
The night was also a big one for Spacey as he was honoured with the Helen Hayes Tribute for his contribution to the arts both as an actor and as a theatre ambassador.
The American Beauty star, who is artistic director of the Old Vic theatre in London, follows in the footsteps of past recipients, including Derek Jacobi, James Earl Jones, Angela Lansbury, Stephen Sondheim and Lynn Redgrave.
Speaking before the ceremony, Spacey told the Washington Post the awards should serve as a reminder for U.S. officials to protect funding for the arts: ""Washington has always had vibrant theatre. I've been a part of it for many, many years. I've done six plays here. So for me, tonight is particularly valuable and important.
""We (need) to be putting much more money into the arts than we are. It's hugely important to our culture, it's important to us as a nation, and I think any nation that doesn't embrace its arts and stand up for its arts is a lesser country.""