The situation in Act 4 of The Crucible is that Mr. Parris is visiting prisoners that "will hang" in the company of Hale who, in Act 3, denounced the hearings and stormed out of the court.
HALE: I denounce these proceedings, I quit this court! He slams the door to the outside behind him.
Marshall Herrick has just had a scene with Tituba and sent her away when Danforth and Judge Hathorne enter, followed by Cheever. Danforth and Hathorne have come on purpose to find Parris as Danforth's first line to Herrick is: "Where is Mr. Parris?" He then asks when Reverend hale arrived. This introduces a discussion of why Hale is present at the jail and whether it is wise to allow Mr. Paris to be "continuously with the prisoners." It is during part of this discussion that Cheever, who accompanied Danforth and Hathorne while carrying a "dispatch case" and the men's writing materials, presumably, at least in part, to be ready in case anyone chooses to confess.
It is Hathorne who opens the discussion about Mr. Parris saying that he wonders if it is good for Parris to be with the prisoners continually. He suggests, when Danforth turns to look at him with interest in his remark, that the reason he should be kept from the prisoners is that he has a "mad look these days." When pressed to explain "mad," he notes that on the previous morning, while passing on the street as Parris left his home, Parris's only reaction to Hathorne's greeting was to begin weeping and hasten away; Hathorne rightly suggests that this looks a little "mad," though Danforth suggests a more reasonable explanation would be that Parris has "sorrow":
DANFORTH: Perhaps he have some sorrow.
This is where Cheever enters the conversation with an explanation of his own. You will note that the information that comes out as the scene progresses provides clues to what Parris might have been weeping about when seen by Hathorne. Cheever's explanation is in three parts. (1) He says that Mr. Parris has always been one to weep in the face of "contention" (i.e., disputes, ill-will, heated disagreement):
CHEEVER: ... Contention make him weep, sir; it were always a man that weep for contention.
[Note that Cheever uses the English of his dialect in using the gender-neutral pronoun "it" to refer to Mr. Parris instead of the correct masculine pronoun "he" and that there are other indications of his dialect: he uses the dialectal "it were always a man that weep" rather than the Standard English "he is always a man who weeps ...."]
(2) He says that Mr. Parris had been "arguin' with farmers all yesterday" about the contention, the disagreement, between farmers about the cows that were roaming the streets since their owners were imprisoned and about what to do with these cows and about who was to take over ownership of these cows. The question of property ownership, even when that property is (to modern Westerns) nothing more than a cow, brings a great deal of contention between those who are vying (i.e., competing or contending with each other) to take over the ownership of the abandoned property.
(3) Because of these two facts firmly established in Cheevers mind--Mr. Parris weeps when confronted with contentious behavior and the farmers embroiled him in contentions over the roaming abandoned cows--he concludes that Parris is "mad looking," as Hathorne put it, because of the cows. Of course this brief, terse statement means, in Cheever's estimation of the situation, that Mr. Parris is "mad looking" because the farmers are disagreeing so disputatiously (i.e., argumentatively) about the correct course of action and about, more importantly, the correct ownership of the cows:
CHEEVER: There be so many cows wanderin’ the highroads, now their masters are in the jails, and much disagreement who they will belong to now. I know Mr. Parris be arguin’ with farmers all yesterday - there is great contention, sir, about the cows.
When Mr. Parris comes from the prisoners, summoned by Marshall Herrick, to join Danforth and Hathorne, after having answered them about Reverend Hale's presence in the jail by saying that "it is providence" (i.e., foreseeing care and guidance provided by God), he summons up the courage to say why he "thought to summon" Danforth, a statement that gives a clue to why he wept when merely greeted by Hathorne. Parris reveals with much difficulty that his niece has vanished. She and Mercy Lewis had been missing three days, after using the "I'm sleeping at her house" double ruse, and had robbed Mr. Parris of "thirty-one pounds" leaving him "penniless":
PARRIS: This be the third night. You see, sir, she told me she would stay a night with Mercy Lewis. And next day, when she does not return, I send to Mr. Lewis to inquire. Mercy told him she would sleep in my house for a night. ... Excellency, I think they be aboard a ship. ... My daughter tells me how she heard them speaking of ships last week, and tonight I discover my - my strongbox is broke into. He presses his fingers against his eyes to keep back tears.
It seems from this that, while Cheever's explanation of weeping due to the contention occurring because of the roaming, ownerless cows being the cause of Mr. Parris's mad look is a partially reasonable one, Danforth's explanation of Mr. Parris's mad look being related to "sorrows" might be the correct explanation after all.
Cheever says that Parris has been arguing with the local farmers who are upset that the cows belonging to people in jail are wandering the area since there is no one to care for them.