The duo from Waterloo, Ont. trail only Americans Madison Chock and Evan Bates, who scored 74.47 to head into the free-dance routine on top of the 30-team field.
Italy's Anna Cappellini and Luca Lanotte round out the top three with a score of 72.39.
Weaver and Poje, who are favoured to win gold, are one of three Canadian pairs who advanced to Friday's free dance.
Toronto's Piper Gilles and Paul Poirier of Unionville, Ont. are in seventh spot after skating a season best 65.90 while Alexandra Paul of Midhurst, Ont. and Toronto's Mitchell Islam scored a season high 64.38 to claim the eighth spot.
Weaver and Poje have won gold in every ice dance competition this season— including both their Grand Prix events, the Grand Prix Final and the Four Continents last month.
They are looking to erase the disappointment of last year’s world championships, where they missed gold by 0.02 of a point.