KIBBY TOWNSHIP, Maine—Weyerhaeuser Co. has cut down more trees than any other American company since its founder started logging before the Civil War. Environmentalists have long treated it as an enemy. Now, the new math of carbon emissions is enabling the lumber producer to cast itself as something quite different: a force for environmental good. Its 10.6 million acres of U.S. timberland act as a giant sponge for carbon dioxide, which Weyerhaeuser says more than compensates for the greenhouse gases it emits by felling trees, sawing them into lumber and distributing wood products. Although Weyerhaeuser is cutting down as many trees as ever and plans to increase lumber production 5% in the next few years, it says its net carbon footprint is negative—so much so that it is offering carbon dioxide storage capacity to other companies.