What were the causes for the increase and sudden decrease of slavery in the US from 1750-1830?

The steady increase was due to the invention of the cotton gin (a machine that cleaned cotton), making the crop more profitable. There was probably a decline about 1808, as this was when the slave trade ended; from then on there were no more 'imports' of slaves, but Americans used the descendants of slaves. (This date to end the slave trade was expected, as it was noted in the Constitution.)

It would be convenient to give all the credit to Abolitionist movements in the US, but state governments strictly limited this by censorship and other means, in the places where the slaves really lived...the South. Also important was that Britain ended slavery in the Caribbean in the early 20th century, and Latin America did at about the same time. So by 1830, the Southern states were the last slave-owning areas in the Western hemisphere.

You may have heard of an incident that happened around 1776. A little war was fought in the British American colonies and colonial rule was kicked out. Suddenly instead of a dictatorial monarchy you had some semblance of a representational democracy and people felt free to protest against things like slavery. So slavery became increasingly unpopular as poor people, who were more likely to identify with the slaves as human beings, had the opportunity to voice their opinions without being sent to the gallows. And the Abolition movement was born.