A member of the girl’s family who spoke on the condition of anonymity to protect her identity characterized the messages as “harmless” but expressed concern that Mr. Weiner had communicated privately with the teenager, a high school junior.

The family was aware that there had been exchanges between Mr. Weiner and the girl but assumed that all of their conversations had taken place on a public Twitter feed. Then a scandal erupted last month over a photo Mr. Weiner sent of himself in his underwear to a college student…

The family member said: “I am angry. This is surreal and unbelievable. It is absolutely crazy. We are just regular people who go to baseball games and basketball games, as ordinary and plain as can be.”