I'm judging him on his lack of leadership/ideas.
They have very troubled soul for a daughter and one of the reasons the wife talks so much IMO is to get him to get creative and try to actively solve their problems.
I have seen this dynamic in other couples over the years. Of course not all.
The sigh is the telltale sign of all husbands worn to a nub by years of criticism from a chatterbox harridan of a wife. Watch and see what happens the next time he opens his mouth. Wrong again!!! Bzzzttt. Just not worth the effort to divorce her but not quite to the blow your brains out stage, so he sits and sighs.