What factors make you sympathize with Sophy in "The Son's Veto"?

Hardy uses description, setting and characterization in the beginning of the story to establish and develop Sophy as a character we readily sympathize with, this despite the fact she is "an invalid" and is ill-spoken: "'Has,' dear mother--not 'have'! ... Surely you know that by this time!"

First, through description, we are acquainted with her hair that is "nut brown" and artfully woven like a basket. This causes much curiosity and admiration in the people sitting behind her at the garden concert. Hardy's description of this aspect of beauty--which is removed from the unsympathetic realm of vanity and pride by the mention that she has no ladies' maid and that her hair adornment is her only accomplishment--creates in the reader the same good will, admiration and curiosity that is created in the audience at the concert.

Later, through characterization, we are acquainted with her open, inviting gaze as curious people file past her at the concert's end. She doesn't mind their curious, though admiring, efforts to see her better and meets their gazes with a look from "soft, brown and affectionate orbs." This psychological characterization of Sophy, when added to her physical description, causes us as well as the characters who found "their way out by passing at her elbow" to sympathize with Sophy. In addition, emphasizing her character more, Randolph is characterized negatively, when we first hear from him, as being "impatient," fastidious and "almost harsh."  

The setting further develops Sophy as a sympathetic character. She is positioned by the bandstand (most often a round gazebo). She is positioned in a "green enclosure" by the bandstand. The green enclosure is a private garden set aside for residents of the surrounding area. This juxtaposition of Sophy to nurturing green, to the melody from a bandstand, to the secluded protection of a private garden all add to the factors that lead us and her fellow concert goers to sympathize with Sophy. [There are many more instances of each of these categorizes for you to identify and analyze.]

[She was] in the front part of a green enclosure, close to a bandstand, where a concert was going on, during a warm June afternoon ... in one of the minor parks or private gardens ...

How does the author create sympathy for Sophy in "The Son's Veto"?

Sympathy is felt for Sophy because she is an honorable person in a setting that does not seem to validate individual honor.  Sophy is not a bad person.  She is constantly being derided by her son, and the fact that she does not retaliate is where one level of sympathy resides. Additionally, Sophy's shortcomings are constantly raised by Randolph, who views her with great contempt.  This is another realm in which sympathy is felt.  Sympathy is natural when seeing a person contantly being  told that their grammar is not correct as they are viewed with scorn and embarrassment 

In the end, one has sympathy for Sophy because she does not do what she wants to do.  Sophy wants to be with Sam.  Yet out of respect for her son, she denies himself.  Sam points this out:  "Still, you can do as you like, Sophy—Mrs. Twycott...It is not you who are the child, but he."  The mother is unable to do what she wants because of fear of her son's reprisals.  When Randolph rejects her wishes, Sophy is left alone with the wishes and hopes that were never meant to be:  " 'Why mayn't I say to Sam that I'll marry him? Why mayn't I?' she would murmur plaintively to herself when nobody was near."  There is much in way of sympathy for someone who shows respect to others and does not receive it in return.  This is where Sophy generates the respect from the reader and how Hardy is able to facilitate it.