Weaver has excelled after being fast-tracked into head coach Rob McCracken's podium squad and he said: "Nobody really expected a lot of me out here but I always really believed I was one of the best.
"I don't really notice the pressure, I just get on with the job. There's a great team spirit and it says a lot about how far we are all progressing that we get three in the finals of the toughest tournament of all of them.
"If you'd told me two years ago that I'd be boxing in a European final this soon maybe I wouldn't have believed you. But now I've got here I feel like I belong and I'm confident of bringing home the gold."
Stalker, who beat world champion Domenico Valentino of Italy in his first fight in the tournament, recovered from a final-round deficit to win 5-2 and secure a final against Albert Selimov of Russia.
Eighteen-year-old Gamal Yafai, in his maiden major championship as a senior, put up a superb display against Russia's world bantamweight silver medallist Eduard Abzalimov but dropped a 2-1 lead in the final round to lose 3-2.
Barry bantamweight Selby was unlucky to suffer a 5-0 defeat to Ukraine's Georgi Chigaev and had to settle for his second consecutive bronze in the event.
Belfast's Barnes secured Ireland's first final place with a comfortable 6-3 win over Spain's Jose de la Nieve at light-flyweight, while middleweight O'Neill beat Bulgarian Mladen Manev 6-0.
But three Ireland team-mates failed to join them. As well as McCullagh, Eric Donovan was beaten 8-2 by Russian Albert Selimov, while Beijing silver medallist Ken Egan blew a 7-2 lead to lose 11-9 to Abdelkader Bouhenia of France.
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