BATAVIA, N.Y. (AP) _ After three days of tantalizing hope and agonizing despair, the sister of Lebanon hostage Terry Anderson is going to Washington to see if a former captive carries a message from her brother.

Peggy Say, looking exhausted but composed, said Monday she was severely disappointed that Anderson was not released from captivity in Lebanon over the weekend. But she said she remains optimistic he will be freed soon.

Boosted by word from freed hostage David Jacobsen that Anderson is healthy, Mrs. Say said she will go to Washington this week to greet Jacobsen and see if he carries any word from Anderson.

Because Anderson has been held 19 months, the longest of the American hostages, including Jacobsen, Mrs. Say said she had anticipated that her brother would be the next one released.

''I'm getting the feeling of being always the bridesmaid, never a bride. We thought it would be Terry,'' she said. ''I'm not devastated. I think it's movement. Any time one person gets out, of course that's good news.

''I'm not ruling out, with Terry Waite's words, that something might happen, as he says, 'soon.' The problem being that I don't know what he means by 'soon.'''

Waite, an envoy from the Anglican Church, has met with the hostage takers and is credited with gaining the release of several captives.

Mrs. Say, who has criticized the Reagan administration's efforts to free the hostages, on Monday offered praise: ''I'm glad to hear they're negotiating. I see that David Jacobsen is very grateful to the government. I certainly am. There's finally movement.''

Jacobsen was held for 17 months before his release Sunday. Anderson, the chief Middle East correspondent for The Associated Press, was kidnapped March 16, 1985.

Mrs. Say said she wondered over the weekend whether her vocal, critical stance during her brother's ordeal had prolonged it by making his captives think he was an asset because of the publicity.

''So, of course my first reaction (to Jacobsen's release) was to blame myself: In some ways have I caused Terry to be held longer?'' she said. ''But friends of Terry and my friends have said, 'If you hadn't been vocal, David Jacobsen would still be there.'

''I feel pretty sure today that it's been necessary. They were the forgotten seven. I don't think they're forgotten now in anybody's mind.''