Alexandria officials said yesterday that after four years of delays a Pennsylvania judge will sentence Frank Weston, the man charged with the 1980 Alexandria murder of Connie Mellon, next week in Pittsburgh for a murder he committed there.

Alexandria Commonwealth's Attorney John E. Kloch said yesterday that the sentencing, scheduled for Wednesday, should finally make it possible for Virginia to extradite Weston and try him for the Mellon killing. Weston has described the crime in detail to police.

"We will work with Pennsylvania officials to get Weston back here as quickly as possible. We want no more delays," Kloch said. He was not certain how long the process would take.

On April 16, 1981, Weston was convicted of murdering Robert Walker in a Pittsburgh shoe store. He has been sitting in Allegheny County Jail awaiting sentencing ever since.

Although Judge Henry R. Smith Jr. of the Allegheny County Court of Common Pleas found Weston guilty of first-degree murder in a bench trial, he refused to impose sentence, saying he felt a jury should decide between life and death. In Pennsylvania, first-degree murder carries a minimum sentence of life in prison.

But in December 1983, the Pennsylvania Supreme Court overruled the judge, and ordered him to sentence Weston. This week, Smith released a March 29 opinion denying a defense request for a new trial.

Weston will now have 30 days to appeal the decision, but it will not affect extradition proceedings, according to Kloch.

Asked why he decided to move ahead with the sentencing, the judge said he had disposed of all the post-trial motions. In the past, Pittsburgh legal authorities have criticized the judge for delays in sentencing convicted felons.

On March 24, The Washington Post reported on the frustrations of Connie Mellon's family and the long series of delays that have prevented Weston from standing trial for her murder. Many officials interviewed in Pittsburgh and Virginia said they thought the Mellon case would never come to trial.

Eleanor Dunham, Mellon's sister, has spent much of the last four years trying to speed the judicial process in the case. "I don't believe it's happening," she said. "I'm ecstatic."

Mellon, who had just moved to Old Town to work for Time-Life Books, was found dead in her house on Oct. 7, 1980. Four days earlier she had been bound, raped and shot in the head.

The police had no suspects until August 1981, when ballistics tests revealed that the gun used by Weston to kill Walker in Pittsburgh on Oct. 4, 1980, also was used to kill Mellon the previous day.