They don't eat all of it anymore, even for Prime members. To the extent they do, it's largely to reduce friction for what is still a purchase that will generally take longer to arrive than going to the store. Plus, it's a nice perk that makes you feel like you're getting a deal.

As for profits, I haven't looked recently, but IIRC profits are mostly:

1. AWS

2. Prime membership fees

The latter drives loyalty and therefore volume and predictability, which allows Amazon to e.g. operate their own mini-UPS in the quest to make money on most parcels. They also rolled back free shipping on everything over the years and use it more surgically and with minimum order sizes.