A jury in Oakland, Calif., ordered Monsanto on Monday to pay a couple more than $2 billion in damages after finding that its Roundup weed killer caused their cancer — the third jury to conclude that the company failed to warn consumers of its flagship product’s dangers.

Thousands of additional lawsuits against Monsanto, which Bayer acquired last year, are queued up in state and federal courts.

The couple, Alva and Alberta Pilliod, used Roundup on their Northern California property for decades. In 2011, Mr. Pilliod, now 76, was given a diagnosis of non-Hodgkin’s lymphoma. In 2015, his wife, who is 74, learned she had the same disease.

The jury, in state court in Alameda County, reached its verdict two months after a federal jury in San Francisco awarded $80 million to a man who claimed that Roundup had caused his non-Hodgkin’s lymphoma. In August, a state court in San Francisco found that Roundup had caused the cancer of a school groundskeeper, awarding him $289 million. A judge reduced that figure to $78 million. That verdict is being appealed.