Bjørgen, who took gold in the women's skiathlon, became the most successful female Norwegian Olympian in history with her win, while Weng took bronze.
Jacobsen, whose brother died on Friday, did not race in the 7.5km + 7.5km skiathlon at the Laura cross country course.
"Sport is sport, but when something like this happens it's hard to focus on the race," said Bjørgen, who won her fourth Olympic gold. "But we stayed together and raced for her brother. Of course it was very emotional. We raced for Astrid, her family and her brother."
Bronze medallist Weng said: "Today I went for Astrid and I promised her to go fast. I had more power today to go for Astrid."
The Norwegian team has confirmed that Jacobsen, who lies second in the overall World Cup standings, will compete in the rest of the Games.