Are there any more reasons for Mrs. Hale and Mrs. Peters not to tell the men that they have discovered Mrs. Wright's motive for killing her husband?
The primary reason that Mrs. Hale and Mrs. Peters withhold the evidence from the sheriff and the attorney is that they do not want it to be used to subject Mrs. Wright to an even more unjust trial than she will already receive. The women are acting as "a jury of her peers" for Mrs. Wright because the legal system of the time did not allow women to serve on juries. Knowing that the prosecuting attorney and the men on the jury are likely to consider the broken-necked bird as merely a "trifle" without seeing the full meaning behind it, they choose to not reveal the evidence they have found while paying attention to what the men consider "trifles." As women, they can put themselves into Mrs. Wright's shoes and imagine the dreadful emotional and probably physical abuse that she had been subject to. To them the dead bird indicates a sort of defense of Mrs. Wright's actions, whereas to the men the bird would provide merely a motive for the murder; they do not want to turn the evidence over to a system that will not interpret it correctly.
Another reason for their decision to withhold the evidence is their own guilt. Society bears some responsibility for Mrs. Wright's crime, and the women perceive that. Mrs. Hale, Mrs. Wright's neighbor and long-time acquaintance, feels personal responsibility because she could have befriended Mrs. Wright after her marriage and checked in on her frequently. That might have provided a way out of the abusive situation for Mrs. Wright. Mrs. Hale laments, "Oh, I wish I'd come over here once in a while! That was a crime! That was a crime! Who's going to punish that?" Mrs. Hale represents the microcosm of society that failed Mrs. Wright.
Mrs. Peters, the sheriff's wife, who was "married to the law," represents the macrocosm of society that also failed Mrs. Wright. What protection did the law provide for an abused wife? Suppose Mrs. Wright had taken the strangled bird to the police station and told the sheriff that she feared for her safety around Mr. Wright. Would he not have pooh-poohed her fears and considered the dead canary only a "trifle"? Even a hundred years after this play was written, it is difficult for women to find support when their husbands, who present a respectable public face, are abusing them in private. But today there are women's shelters and hotlines. In those days when women did not even have the right to vote, they were nearly powerless. Mrs. Peters, who is evidently moved by Mrs. Hale's expression of guilt, no doubt also shares a sense of responsibility for what Mrs. Wright had been driven to do.
In addition to their desire to not enable an unjust legal system, the two women withhold evidence because of a sense of personal and societal culpability for the crime.