Although it feels like the dentist's drill must be gouging away huge parts of your tooth, the reality is that most of the time the dentist is barely touching your tooth with the drill. Imagine you were trying to remove the paint from a delicate piece of furniture. (This mental image has helped me a lot with dealing with the drill. I remind myself that she's barely applying any pressure at all...)
Because of the variability of the size and speeds of various bits, it's almost impossible to tell "how much tooth" the dentist is removing based on how much time the drill is running. There's also a lot of precision work that takes lots of time but doesn't really remove much dental matter. In my experience, having amalgam removed takes a long time-- I think it's hard on the drill and also they tend to use lots of water.
If you're interested, you can ask to see the x-rays, and your dentist can show you. But really you probably won't understand; it'll just look like a white spot on the x-ray. A more interesting question would be to ask how strong the remaining tooth is, and if there's any chance of needing a crown or additional restorative work later. The crown of a tooth is pretty resilient and can usually withstand a pretty big filling without adverse effects.
As for the "fat tooth" feeling, give it a couple of days. Your tongue can be pretty sensitive to new things showing up, and will usually stop noticing within a few days. If you still feel like your bite is off or something is rubbing against something else, the dentist should be able to make a quick adjustment to the filling to correct. For fillings on the biting surface of the tooth, this is pretty common.