Mr. Weaver, who entered politics only in 2013, when he won a seat in the provincial Legislature, will have to do some delicate maneuvering when it comes to pushing other items on his party’s agenda.

The New Democrats favor positions in line with the Greens, including the limiting of mining and forestry. They do, however, conditionally support the liquefied natural gas initiative.

The economic importance of the forestry, pulp and paper industries to British Columbia may make it difficult, if not impossible, for the New Democrats to adopt any Green Party position that might limit production in the interests of sustainability and the mitigation of climate change.

In 2015, according to the most recent statistics available, more than 65,000 people worked in the sector, and the forestry industry produced 10 billion Canadian dollars in exports for the province. Many forestry workers are members of labor unions that were part of the initial formation of the New Democrats and that are major donors to the party.

The sector’s importance was clear when Ms. Clark suggested she might retaliate against the United States after the Commerce Department imposed a new round of duties on Canadian lumber last month in a decades-old trade battle.

In addition to working with the New Democrats, Mr. Weaver will face pressure from his own party.

“Environmentalists will definitely be reminding the Green Party where their base is,” said Emma Gilchrist, the executive director of DeSmog Canada, an environmental journalism organization in British Columbia. “They will have a very slim majority. It’s not going to be easy to get things done.”

Still, Mr. Weaver’s bargaining position in the Legislature gives him leverage.

“There’s no question that Andrew Weaver is in an exceptional position of power,” said Maxwell A. Cameron, a political scientist who has studied minority governments in his role as the director of Center for the Study of Democratic Institutions at the University of British Columbia. “Not only does he get to choose what party he supports and put it in office, to some extent he gets to determine its policies.”