The idea that we should regard this extensive record in the career to which Weiner has dedicated his entire adult life as somehow fake, and his after hours twittering as revealing his “real” character just doesn’t make a ton of sense.
One way to see this through an extreme case is perhaps just to observe that the demands of being President of the United States are straightforwardly incompatible with being a model husband and father. The hours, the travel, and the stress just don’t make it add up. But it can’t be the case that all Presidents of the United States lack the requisite character to be President of the United States. It has to be the case that the kind of character that matters for a public official isn’t the same as the kind of character that matters to be a good husband and father. After all, you want a responsible public official to neglect his family and friends (“hard-working”), to display a certain kind of ruthlessness and cunning (“negotiation”), to be a bit of a phony in certain situations (“diplomacy”), and all kinds of other things that don’t carry over straightforwardly from personal life to public affairs.
Well, that's simply an instance of the general Machiavellian principle, as expounded by Isaiah Berlin; the qualities required of a good statesman are not simply different from those required of a good private citizen, they're incompatible. For example, being a war criminal is pretty much part of the job description for being an American president. Or, in the words of Sydney Smith,
"You spend a great deal of ink about the character of the present prime minister. Grant you all that you write — I say, I fear he will ruin Ireland, and pursue a line of policy destructive to the true interest of his country: and then you tell me, he is faithful to Mrs. Perceval, and kind to the Master Percevals! These are, undoubtedly, the first qualifications to be looked to in a time of the most serious public danger; but somehow or another (if public and private virtues must always be incompatible), I should prefer that he destroyed the domestic happiness of Wood or Cockell, owed for the veal of the preceding year, whipped his boys, and saved his country."
I have no idea who Wood and Cockell are, which is mildly irritating, not to say, for a history buff, humiliating.