Fairweather finished fifth in her semifinal but was among the fastest eight qualifiers so will have a chance to swim for a medal tomorrow morning.
The Black Ferns won their first two games of the tournament this morning - besting both China and Canada - they take on Fiji in their final pool match early today.
But several New Zealand athletes had a tough time at the Olympics overnight and early on Monday.
Surfer Saffi Vette was eliminated from the Games in her second round heat in Tahiti.
Lulu Sun lost her first round singles match to Ukraine's Marta Kostyuk and her doubles match with Erin Routliffe was delayed again by rain.
Gymnast Georgia Rose-Brown missed out on the finals, Luuka Jones missed out on the medals in the kayak singles, and Sammie Maxwell finished 8th at the mountain biking.
Swimmer Lewis Clareburt made it to the 400m individual medley final but came 6th.
The race was won by French swimmer Leon Marchand, a "megastar" who broke the Olympic record.
RNZ host Nathan Rarere Rarere, who is in Paris, described Marchand as the "best to ever do it".
"It's tough. I don't have too many words right now," Clareburt said after the race.
"I'm not sure, something just didn't click today. That's sport. You train your whole life for this one moment, and if you don't get it right, that thing happens.
"I didn't want to be in this position standing here, saying this right now, but someone has to lose and today it was me."
