He served as assistant pastor until 1931 when he was appointed the archdiocesan director of the Society for the Propagation of the Faith.

On November 22, 1929, Pope Pius XI conferred the title of "Right Reverend Monsignor" on Father Sweeney.

On May 20, 1941, he was appointed the first bishop of the newly erected Roman Catholic Diocese of Honolulu.

His funeral liturgy was held at his home parish of Saint Paul in San Francisco.

At his request, he was buried with his parents in a family crypt in Holy Cross Cemetery in Colma, California.