Part of the answer that you are looking for is the First Great Awakening, a series of religious revivals beginning in the 1730s and continuing for several decades. Part is the Second Great Awakening, beginning the late 1700s and continuing into the early 1800s.

First, some background: You are correct in noting that the Northern colonies were initially more religious than the Southern ones. Massachusetts and its neighbors were settled in the 1600s by Puritans who rejected the Anglicanism of England.

In the South, the dominant church in the 1600s was the Anglican church, but Virginia society was very hierarchical and competitive, and was much less oriented around religion than New England.

However, by the end of the 1600s, preachers in the North were saying that religion was in a sad state of decline. Ministers said that the first generation of settlers had been very religiously committed, but that later generations were increasingly focused on money and business. (Whether this story of decline, which historians refer to as the "declensionist narrative" is accurate is a subject of debate.)

At any rate, by 1700, when these preachers looked at America, they thought that Christianity had once been great (but declined) in New England. They saw the South as basically spiritually dead.

The First Great Awakening (beginning in the 1730s and continuing for decades) featured great revivalist preachers like George Whitefield and Jonathan Edwards who wanted to revive Christianity in America. Many of them were great speakers, and they travelled around, preaching to great crowds. (In his autobiography, Ben Franklin described watching George Whitefield preach. He was extremely impressed, and although he was not converted, he was so moved by the experience that he dumped all the money he had on him in the collection plate!)

First Great Awakening preachers aimed to touch the hearts of those who listened. They aimed very much at feeling and emotion, and they were extremely good at working up strong emotions in the crowds that listened to them. Many sources from the day report people falling into trances, being struck down to the ground, or crying uncontrollably. They also preached to anyone who would listen -- including poor whites, Native Americans, and enslaved Africans and African Americans.

These revivals were intensely controversial, and the churches divided over them. Tons of people were extremely excited about these revivals, and would travel from miles around to hear one of these famous preachers. But what did it all mean?

Two schools of thought arose immediately. Door #1 is known as the "Old Lights." Old Lights included Anglicans, Congregationalists (the descendants of the Puritans) and some Presbyterians. They basically rejected the revivals. They said, "Yes, it is very easy to get people emotionally worked up, but that isn't true religion. Where is knowledge of the Bible in this? Where is love of your neighbor? Where is living a dutiful life?" Christianity, they said, isn't about "oh, I have ecstatic feelings," or "I fell into a trance," or "I had a conversion moment," but about a sober life of duty. (I'm being a little harsh on them: they did believe that people could and did have religious experiences, but they placed much less emphasis on these experiences.)

Door #2 is the New Lights (Baptists, Methodists, and some Presbyterians). The New Lights thought that the intensity of the revivals proved that they were indeed the work of God. They said that God was pouring out his Spirit on young and old, rich and poor, and white and black. They criticized the Old Lights as spiritually moribund.

Who wins? In the North, the Old Lights were strong enough to largely maintain their hold, although the New Lights certainly had many converts. The Old Light churches benefited from having a more highly-churched population and a higher degree of pre-existing religious commitment to Congregationalism. So they stuck with a more staid and generally conservative form of Christianity.

But in the rest of America (and especially in the South) the New Light wins. The Baptists and Methodists eventually became the dominant churches there.

Why?

Well, I'm simplifying here (and combining the First and Second Great Awakenings). But the New Light Baptists and Methodists had a lot of advantages that helped them to thrive in the South and West.

1. Unlike the Anglicans, New Light churches didn't necessarily require a highly educated clergy. (Anglican priests can only be ordained by bishops, and there were no bishops in America until after the Revolution.) In the 1800s, you will see the rise of the "farmer-preacher" in Baptist circles: basically, a farmer who thought he felt a call to preach and answered it. If he could gather a congregation, then boom! He's a minister. So in the 1800s, there will be lots more Baptist preachers than Episcopal (Anglican) priests.
2. The New Light churches placed less reliance on religious authority all the way around. While Anglicans and Congregationalists thought that extensive education was necessary to interpret the Bible rightly, Baptists and Methodists were more inclined to say that its meaning could be understood by anyone. The South and West in the 1800s were very rural, and this idea would appeal strongly to people who might not have regular access to a church.
3. This egalitarian sense fits in very well with American culture generally in the first half of the 1800s. This time period featured a general rejection of claims to elite status (among whites) in a lot of areas, which explains (for example) why non-landowning white men were suddenly permitted to vote. A church that says, "Of course anyone can read and understand the Bible for himself or herself!" held a strong appeal.
4. In the 1800s, Baptists and Methodists tended to share a view of salvation called Arminianism. It basically says, "God wants to save everyone. Accept the free gift of salvation that God offers through Jesus, and you will be saved! Also, you can be sure that you are saved!" This is much more appealing than Puritan predestination.
5. These churches were also capable of crossing lines of class and race. They appealed strongly to poorer whites, African-Americans, and (to a much lesser extent) even Native Americans. The idea that God can and does touch people of all ranks, and that they can have true, emotional religious experiences was extremely appealing. It would be much easier for a poor white man or a black man to become a Baptist preacher in the 1800s than for him to become an Episcopal priest, for example. (This doesn't mean that these churches generally rejected earthly hierarchies of race and class. Most didn't. But they did say that God saw all souls as equally valuable, whatever one's position on earth.) Historians have argued that these beliefs allowed marginalized people to claim a kind of dignity and status that wasn't likely to be available in Old Light churches.

Readings:

Two places to start would be Thomas Kidd, The Great Awakening: A Brief History with Documents (2007) and Nathan Hatch, The Democratization of American Christianity (1991).

If you want to read a very unhappy Anglican minister criticizing rural North Carolinians and their new religious ideas, Charles Woodmason is always fun: https://teachingamericanhistory.org/document/the-journal-of-reverand-charles-woodmason/

Among the most famous Great Awakening sermons is "Sinners in the Hands of an Angry God," in which Jonathan Edwards tries to stir people up to fear and repentance:

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1053&context=etas

And here is Benjamin Franklin, talking about George Whitefield's skills as a preacher: http://nationalhumanitiescenter.org/pds/becomingamer/ideas/text2/franklinwhitefield.pdf

The origin of the Bible belt has been discussed in much detail before (by a now-anonymous author and several others), as well as in several other threads. Using the sub’s search feature may benefit you in learning more about this.