"There you go" is idiomatic in British English, but doesn't really have one single meaning. In this context though, it is not really either of the definitions you found.
In this particular context, it shares at least some of the meaning of these similar expressions:
- "There you go"
- "There you have it"
- "That's how it is"
In your example, "there you are" is being used to express the fact that the speaker cannot change the situation he has just described and has resigned himself to accept it. He appears to have some odd habits, and as a consequence, his wife thinks he is "mad" (meaning insane) and he accepts that he cannot do anything to change her perception.
The Cambridge dictionary gives this example for one definition of the similarly used-used expression "there you go":
We didn't win the competition, but there you go - we can always try again next year.
You can see the similarity to your example. The speaker has presented an unfavourable situation, and "there you go" expresses their acceptance of it.