Wester is to be installed as archbishop of the Santa Fe Archdiocese on Thursday. His appointment by Pope Francis was announced in late April.
It will be several months before Wester's replacement is named; he will return to Salt Lake City's cathedral June 26 to ordain two men to the priesthood.
Wester used the story of the two brothers — the older one put his brother in a headlock when he said he loved his big brother — as a human reflection of the trinity. Sunday was Holy Trinity Sunday for Catholics worldwide.
While theological explanations of the Trinity are "mere glimpses," God as a communion of three persons can be seen throughout the Old and New testaments, Wester said.
"God is, in his very nature, relational," Wester said. "In order to speak about God, we must speak about the Father, Son and Holy Spirit."
Wester thanked Utah Catholics for their generosity of time, talent and treasure. "You have helped me to grow as a person and a bishop."
When he first arrived, Wester said, Monsignor Terrence Fitzgerald, then-vicar general for the diocese, told him to expect Utahns to be hospitable.
"I've had that word in my heart and brain ever since," Wester said, "and he couldn't be more correct."
The cathedral choir, orchestra and Madeleine Choir School choristers performed a Mozart Mass and the moving piece "Abide in Me," commissioned in 2007 for Wester's installation as the ninth Catholic bishop of Salt Lake City. "Abide in Me" is Wester's episcopal motto.
Students from each of the diocese's schools brought single roses to the bishop as gifts before communion, and 20 priests and deacons from around the diocese helped celebrate the Mass.
Wester said he had seen so many examples of selfless giving by Utah Catholics, but Lynn Johnson, a deacon at the cathedral, recalled later that Wester led by example.
The two were once late for a parish visit in Draper and driving through rush-hour traffic in downtown Salt Lake City. A heavy man in a wheelchair had tipped over. Pedestrians streamed past, ignoring his predicament.
Wester ordered Johnson to pull over, although there was nowhere to park. It took the two of them — and a pedestrian Johnson recruited — to lift the man back into his chair.
It was then the man saw Wester's clerical collar.