There were two main points offered in favor of slavery at the Constitutional Convention.
First, there was the fact that slavery had been accepted by the whole world in all times and places. It had been accepted by the Greeks and the Romans (who were held in great respect by the Founders). It was accepted by France and Britain and other modern countries. Therefore, the implication is, slavery coiuld not be wrong.
Second, there was the fact that slavery was important for the national economy. It was pointed out that the Southern states could not do without slaves. It was also pointed out that more slaves led to greater production by the South. This production was generally exported and would help to enrich the country.