Gossip began as a religious relationship, not a social habit.
Old English godsibb joined god with sibb, an old word for "related" or "akin." A godsibb was a sponsor at a baptism, a godfather or godmother, tied by a spiritual bond to the child, the parents and the other sponsors. In effect, God-kin.
The bond made the godparents close to the family, so the word spread. By about 1300, Etymonline says, it meant a familiar acquaintance, friend or neighbor. It leaned especially toward the women friends invited to attend a birth. Word Histories quotes Thomas Fuller, writing in 1662, who still speaks of "all the Gossips present at their Mothers labours."
Then the meaning shifted from the person to the conversation. Etymonline dates the sense of anyone engaged in familiar or idle talk to the 1560s. The verb, "to talk idly about other people's affairs," followed in the 1620s. The step to the noun for the talk itself, "trifling talk, groundless rumor," is recorded by 1811.
The path seems natural: friends who sit together for hours and chat will talk about the people they know. Word Histories lays out the same path: godparent, then friend, then a woman's friends at a birth, then malicious talk.
French offers a close parallel. Commère comes from Christian Latin commater, "godmother." It also came to mean a female friend, and then a woman who talks about other people's private lives. Its masculine partner compère never took on the negative sense. The French word for malicious gossip is commérage.
The same Old English sibb survives in sibling. Etymonline's entry for god adds that God is not related to good, despite a long-held popular belief.
So the word for rumor traces back to a church ceremony. Each time someone is described as a "gossip," the older and warmer meaning, a trusted companion, is still inside it.