Start researching the "Half-Way Covenant".

The Salem Witch Trials was essentially a last flexing of the weakening political muscle of the Puritan movement in New England, and not an indication that it was strong and healthy. Essentially, what happened was that the Puritans came over with the ideal of a church based on Biblical scripture and nothing else, and free of the political influence of kings and lords. In practice, though, they quickly began fighting among themselves of exactly what that all meant, which led to a schism between Plymouth and the political/religious faction that supported Roger Williams, and they left and founded Rhode Island in 1636. And then Anne Hutchinson began having disagreements with her congregation, and was banished to New York in 1638, so her political/religious allies left not long after and founded Connecticut later that same year.

There was some stability for a while, but by the 1660s, there were more threats of schisms, so a movement to establish the "Half-Way Covenant" began. Before the Half-Way Covenant, to have any rights as a citizen of Plymouth or Massachusetts, you had to be a member of one of the church congregations, and to be a member, you had to take a strict oath and adhere to a rather pious life that not everyone in the colony agreed with. So a lot of people were electing to just forego the church altogether, and in light of what had happened in the late 1630s and early 40s when there was an exodus of many of their citizens, this latest movement concerned the political leaders of Plymouth and Massachusetts enough that they began considering giving rights to people who would not join the church on the current congregations' terms, so long as they vowed not to interfere with church matters in any way, such as by speaking out against it or trying to establish their own congregations, etc. There was a bit more to it than that, but that's the gist of it.

But the Puritan movement was based on a Congregationalist ecclesiastical polity. That is, unlike the Catholic Church which had a top-down structure with the Pope's word being canon law, and unlike the Anglican Church which had a top-down structure with the King's word being canon law, and unlike the Presbyterian and Dutch Reformed churches which had a presbyterian polities where each congregation elected elders who would then attend an annual meeting called a synod and that meeting would establish canon law, the Congregationalists believed that each parish church should be the master of their own congregation's destiny. They were essentially independent from each other, and no other church or no other authority could tell them what to do. They would have annual synods, just like other denominations, and they would discuss church matters there, but nothing that the synod did had any direct effect on any individual church if they didn't want it to.

So when the Half-Way Covenant was proposed at one of these synods in the 1660s, it was met with a lot of backlash by congregations who didn't want to adopt it, and many of them did it. More did than not, but it was a bone of contention for the next several decades, and it is seen as the beginning of the end of the Puritan movement in New England being united under one political/religious philosophy. They began to separate out into factions, with some congregations becoming more progressive on church matters, and others remaining conservative.

The other important event that occurred was the Glorious Revolution of 1688 back in England, which spilled over into the American colonies. King James II had succeeded to the throne in 1685, and he was Catholic and was determined to institute Catholic rule over England and its colonies. But the American colonies did not want this--they all hated the Catholics, and the Puritans especially. The Puritan movement had originally been a movement against the Protestant movement led by Henry VIII when he left the Catholic church. The Puritans were happy about this, but didn't think the Protestants had gone far enough--they'd just replaced one political body with another (hence their polity of Congregationalism as opposed to the Anglicans' top-down "episcopal" polity with the King as the head of the church).

In order to control the colonies and prevent them from rebelling, and in all likelihood as a first step to convert them to Catholicism, James II revoked all the colonial charters from New Jersey on north, and united them as the Dominion of New England in 1686. The colonists were not happy about this, so when James was overthrown by his daughter and son-in-law William and Mary at the invitation of Parliament in 1688, the Puritans in Massachusetts and Plymouth organized a revolution of their own. They kidnapped the governor, Edmund Andros, and refused to release him until the Dominion was disbanded.

They got their way, but the previous colonies were not restored exactly. Parliament was weary of the hardliners in Plymouth, particularly, since their basis in government up to that time had not been a sanctioned charter signed by the monarch, but it had been the Mayflower Compact signed by the people (a fact that would come back to haunt them during the American Revolution). And under the authority of the Mayflower Compact, the people of Plymouth had essentially run their colony as a Puritan theocracy. So when the Dominion of New England was disbanded, Parliament issued a new colonial charter that united Plymouth and Massachusetts Bay under a single charter (they had been separate colonies before) and in this charter, the colonists were forced to allow more religious tolerance than they had before. Anglicans, Presbyterians, Quakers, and others would be able to live and worship as they pleased and still get the rights afforded to all citizens (voting rights for adult men, etc.) without interference from the Puritan Congregationalists. This was agreed to, which further reduced the power that the Puritans had once had before the 1660s when they were a united political movement.

The 1700s, then, proceeded in Massachusetts as one of religious disunity, and initially as one of political disunity as well, as evidenced by the Salem Witch Trials late in the 1600s. It happened under the authority of a Puritan political majority, but the backlash pretty much guaranteed that they would never enjoy such a majority again.

Thus, the first half of the 1700s in Massachusetts was colored by previously-disenfranchised political factions getting a voice in government for the first time, which led to disunity except thst there emerged a unity to reject the 17th Century monolithic political/religious structure. These factions then came together during the lead-up to the Revolution, as there seemed to be a repeat of what had happened in the leadup to the Glorious Revolution: Parliament issued the Massachusetts Government Act in 1774, which dissolved the colony's government and put them under martial law. The legislature then relied on an argument that their charter could not legally be revoked, since their government stemmed from the Mayflower Compact, which the King and Parliament had not been a party to, and the replacement 1691 charter had not stipulated that all rights not explicitly written about in the charter reverted back to Parliament and the King, as was the language in all the other colonial charters of the 13 Colonies. This hadn't been put in there because Parliament was afraid back in 1691 that it would be rejected otherwise, thus, Massachusetts began talking about the rights of the people that could not be infringed upon, and Parliament and the King were acting like tyrants by taking those rights for themselves.

Anyway, I guess that goes beyond your question.

TL;DR: The Puritans had control for about forty years, but even within that period, there were severe schisms that led to the founding of other colonies. In order to prevent further schisms and unrest, the church began debating issuing the "Half-Way Covenant" which would offer some rights to non-church members, and the infighting over this led to division within the Puritan movement. Shortly after the Catholic king James II took over the throne and tried to take way Plymouth and Massachusetts' autonomy, the people of Massachusetts and Plymouth rebelled, and the result was that they got some of their autonomy back, but the Congregationalist churches had much of their power taken away since they had to agree to much more religious tolerance than before in order to receive a new colonial charter. The Puritans' political power died out in the decades that followed. And due to the Puritans' Congregationalist philosophy of religion, it was not possible any longer to keep the individual Congregations united under a single conservative religious philosophy as they had been early in colonial history. The politics of government and religion split the congregations apart in the first half of the 1700s, and the Puritan movement lost its influence.