What does Hillary Clinton’s “a little note of levity at 7:15” at night mean?

During the night of the attack in Benghazi, Libya in which four Americans were killed, Hillary Clinton, then Secretary of State, was monitoring events with her staff at the offices of the US Department of State. At some point, she left to go home; her staff remained at the offices. Clueless Representative Martha Roby asked Clinton if she had been alone in her house, to which Clinton replied in the affirmative. "All night?" Roby asked, apparently unaware that her question was a double entendre, hinting that Clinton might have spent the night in the company of a lover.

The question was ridiculous. Alone or not, what possible difference could it have made? The possibly salacious wording elevated the question to the farcical, and Clinton cracked up. But Roby didn't understand what a fool she'd made of herself and said, "It's not a laughing matter," referring to the events in Libya. But what Clinton (and everybody else with a sense of humor) was laughing at was the ridiculous Roby herself and by extension, the whole Select Committee and its shenanigans.

Levity is light-heartedness or frivolity, and Clinton's reference to the time of day was to underscore that after nine hours of testimony without a single germane question, if the silliness of the Committee's wasn't evident to everyone, then Martha Roby's maladroit question made it so.

The "I'm sorry" wasn't to suggest remorse on her (Clinton's) part but was an ironic aside to indicate how pathetic Roby was. Clinton had used the same trope earlier to put down another clueless Committee member, Jim Jordan, when she said in response to him, "I'm sorry that it [Clinton's testimony] doesn't fit your narrative, Congressman. I can only tell you what the facts were."

Note means:

A particular quality or tone that reflects or expresses a mood or attitude: ‘there was a note of scorn in her voice’ ‘the decade could have ended on an optimistic note’.

[Oxford Online Dictionary]

Levity means:

a lack of seriousness, an amusing quality, excessive or unseemly frivolity, lack of steadiness : changeableness

[Merriam-Webster]

7:15 is the exact time that either the question ("The whole night?") or the answer ("Well, yes, the whole night.") was uttered.

She was being sarcastic using "a note of levity" in response to Martha Roby's question of "The whole night?", as she considered the question of asking her if she was alone "the whole night" was irrerelvant, frivolous, amusing, and lacking seriousness.

She was being sarcastic. The hearing, which many view as a witch hunt, an entirely partisan attack by Republicans in Congress, was already in its ninth hour, as the article says, and Mrs. Clinton's comment was to say that it was the single "lighter" moment in the whole proceeding.