They make plenty of money, but that is then invested back into expanding the business, so it's more accurate to say that they don't make much profit at this time.
If that were true they would not be slowly making the service worse to try to eek out some money. "Add On Items" Removing items from being next day eligible with Prime etc.. As someone who orders from Amazon all the time (daily) I have seen a drastic downgrade in the service from what it used to be. Feels more like Walmart then Amazon these days.
I haven't looked at Amazon's numbers, so I don't know the actual values involved, but "profit" includes money that is then "invested back into expanding the business".