I am 1 week into my pre-op diet and down 16 pounds. What is the average loss during those 2 weeks.

Are you only having fluids? What is your pre op Diet?

Drinking lots of water. Low carb high protein diet. I went to a nutritionist told them i need to shrink my liver and what surgery i was having and paid for 2 weeks of prepped meals

It is hard to say what an average is; every body and pre-op seems to be different. But it sounds like you're doing well.

How long is a piece of string?
There are several different preop diets, and many more factors that dictate the rate of weight loss including starting weight, age, activity level, water retention, hormones, stress, the list goes on.
But the important thing is doing what you are doing and sticking to the plan no matter what the results.
Often people who drop weight fast become relaxed with the program and it hurts them in the long run.

So while you early success is awesome, be careful not to let it work against you.

Glad you are having success, keep up the great work!