A jury Monday awarded $2.055 billion to a California couple who blamed Bayer’s Roundup weedkiller for causing their cancer, the largest such verdict to date and one that adds significant pressure to a company struggling to contain the fallout from last year’s acquisition of Monsanto Co.

The verdict by the Northern California jury is the third straight trial loss for Bayer over the safety of Roundup. Bayer is facing a revolt from shareholders over the Monsanto deal, which exposed Bayer to some 13,400 claims tying Roundup to...