Why did the overseer leave Solomon to hang?

The overseer isn't sympathetic to Solomon, especially as his current predicament is a result of insubordination.

However, his job is to ensure that the slaves remain obedient, but more importantly alive as they are the property of Mr Ford, who "has a debt to be mindful of".

After scaring off Tibeats, he seems to evaluate the situation and decides to leave Solomon on the lynch, ostensibly to teach him some kind of lesson without the price being his mortality.

The only reason that Mr Ford even takes him down is because he is a tentative abolitionist: although a slaver himself, he obviously holds slaves in a higher regard than many other plantation owners, as demonstrated by his attempt to keep Eliza's family together.

Mr & Mrs Ford are deeply conflicted people, and perhaps their worldview is best demonstrated by the actions of Mrs Ford during this semi-lynch sequence:

Mrs Ford comes out onto the veranda, and watches Solomon struggling to keep his footing. She is unwilling to go down and help him (perhaps because she doesn't consider it her place to do so) but she also can not bear to watch him struggling, so she goes back inside the house, closing the door behind her.