Famigliuola is a diminutive form of famiglia (family), meaning 'little family'. The suffix -uola adds a sense of smallness, endearment, or sometimes even a touch of quaintness.
In the song, the narrator sees an old friend with his famigliuola, highlighting a contrast between the friend's settled life and the narrator's own wandering existence. It's a charming and slightly old-fashioned word that evokes a specific image of domesticity.
Diodato sings about the quiet distance between how you feel and what you let people see.
The song opens with the people around him. His mother worries and tells him she does not know what will become of him, alone in this city. A friend, now with a little family of his own, warns him that time flies and that you only get one life. He hears both, and carries on anyway, still out at night with people who live the way he does, knowing that tomorrow will come asking why.
The sunglasses in the chorus are the answer to that question. They are worn so nobody can see what he and his friends carry deep down in their eyes. Behind them he can pour everyone a drink and reply to every "how are you" with "everything's fine", which is the easiest thing to say and the least true.
The second verse gives away what the tiredness is really about. He remembers a story the two of them used to tell, about growing old together in front of a beautiful fireplace, and admits that only the smoke is left of it. Then he offers the one honest invitation in the whole song: if you feel the same way I do, come and find me tonight.
It is a song about putting on a face in public, and about how much lighter it gets when one other person knows you are only pretending.