"oh, what burden, Lord, to be the father of a grown-up daughter"- Who is the father? Who is the daughter and why she is a burden to the father?

Here Chubukov is the father in Anton Chekhov's hilarious farce, "The Proposal".
           
           The daughter is Natalya.

 In a patriarchal society a girl- child is often seen as a burden. It is an embarrasing duty of a father to find groom for his daughter. He feels the pressure of society to get his daughter married. But he is always puzzled by the whimsical mood of his daughter. When Lomov comes with a marriage proposal, Chubukov is greatly pleased. But Natalya is engaged in a bitter quarrel with Lomov. She drives Lomov out from their house. Again, when Natalya hears Lomov's proposal, she is desperate to be married and asks his father to bring Lomov back. Then out of utter hopelessness, Chubukov makes this speech.