The term translated as “curse” is “blaspheme,” that is, to speak against someone in such a way as to injure or ruin his reputation. A few verses earlier the angel had talked up God’s reputation with his claim that God’s judgments were “just” (Revelation 16:5), a claim the altar had echoed (Revelation 16:7). Despite that heavenly praise for God’s righteous judgments (the plagues), the worshippers of the beast blasphemed God, tried to ruin his reputation. Here is forceful disagreement between those of heaven and the beast’s worshipers on earth—as is to be expected given Satan’s eviction from heaven (Revelation 12:9).
11 and cursed the God of heaven for their pain and sores. They did not repent of their deeds.