How does Watson know that Barrymore is lying about his wife crying at night in The Hound of the Baskervilles?
Barrymore says his wife did not cry, but Watson can see her eyes.
In his first case without Sherlock Holmes, Watson is in over his head a bit. His task is to look for clues and report back. He has no idea how close Holmes really is, and he is doing his best to solve the case his way.
The Barrymores are the main servants at Baskerville Hall, “the husband acting as butler and the wife as housekeeper” (Ch. 2). Watson is staying at the Hall, and he hears crying in the night. He tells them that he heard the “sob of a woman.” Barrymore says there are only two women in the house.
And yet he lied as he said it, for it chanced that after breakfast I met Mrs. Barrymore in the long corridor with the sun full upon her face. But her tell-tale eyes were red and glanced at me from between swollen lids. It was she, then, who wept in the night, and if she did so her husband must know it. (Ch. 7)
Watson is kind of mixing his words a little here. First he says Barrymore lies, and then he says that maybe he does not lie, maybe he just does not know that his wife is crying.
Watson describes Mrs. Barrymore as “a heavy, solid person” but “inclined to be puritanical” (Ch. 8). He becomes suspicious of the two of them when he realizes that she has been crying.
I heard her sobbing bitterly, and since then I have more than once observed traces of tears upon her face. Some deep sorrow gnaws ever at her heart. Sometimes I wonder if she has a guilty memory which haunts her, and sometimes I suspect Barrymore of being a domestic tyrant. (Ch. 8)
So at first he suspects Mr. Barrymore is the one causing her to cry, since there is “something singular and questionable in this man's character.” He decides to investigate. He finds Barrymore walking around at night, “very slowly and circumspectly,” and this is of course sneaky behavior. The man is up to something. Watson watches, and he finds out what.
Barrymore was crouching at the window with the candle held against the glass. His profile was half turned towards me, and his face seemed to be rigid with expectation as he stared out into the blackness of the moor. For some minutes he stood watching intently. (Ch. 8)
Watson doesn’t confront him at the moment. He thinks about it. Writing to Holmes, he says he suspects perhaps “love intrigue” since Barrymore seemed to be looking out to someone (Ch. 9). Watson gets Henry Baskerville involved in the sleuthing, and his decision is to sack the two of them, saying they are “deep in some dark plot against” him (Ch. 9). It is then revealed that her brother, an escaped convict, is out on the moor and they have been helping him by giving him food.
Holmes often says that Watson has a good mind, but not good enough. He often comes to the wrong conclusion. In this case, he is on his own, trying his best to look for clues and both convey them to Holmes in the most meticulous fashion and also determine what they mean. Sometimes he gets them wrong. They turn out to be the most delightful red herrings (false clues), and big wastes of time. Holmes might have solved this one much more quickly, but Watson got there eventually.